Gravitational wave

For the different concept in hydrodynamics, see Gravity wave. Fluid dynamics is the sub-discipline of Fluid mechanics dealing with fluid flow: Fluids ( Liquids and Gases in motion In Fluid dynamics, gravity waves are waves generated in a Fluid medium or at the interface between two media (e

General relativity

$G_{\mu \nu} + \Lambda g_{\mu \nu}= {8\pi G\over c^4} T_{\mu \nu}\,$

Einstein field equations

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Kepler problem · Lenses · Waves Frame-dragging · Geodetic effect Event horizon · Singularity Black hole

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In physics, a gravitational wave is a fluctuation in the curvature of spacetime which propagates as a wave, traveling outward from a moving object or system of objects. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 The Einstein field equations ( EFE) or Einstein's equations are a set of ten equations in Einstein 's theory of General relativity in which the General relativity (GR is a Theory of Gravitation that was developed by Albert Einstein between 1907 and 1915 The mathematics of general relativity refers to various mathematical structures and techniques that are used in studying Albert Einstein 's theory of General The Kepler problem in general relativity involves solving for the motion of two spherical bodies interacting with one another by Gravitation, as described by the theory of A gravitational lens is formed when the light from a very distant bright source (such as a Quasar) is "bent" around a massive object (such as a cluster of Albert Einstein 's theory of General relativity predicts that rotating bodies drag Spacetime around themselves in a phenomenon referred to as frame-dragging The geodetic effect represents the effect of the curvature of Spacetime, predicted by General relativity, on a spinning moving body In General relativity, an event horizon is a boundary in Spacetime, an area surrounding a Black hole or a Wormhole, inside which events cannot A gravitational singularity (sometimes spacetime singularity) is approximately a place where quantities which are used to measure the Gravitational field become A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. In Mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. Gravitational radiation is the energy transported by these waves. Important examples of systems which emit gravitational waves are binary star systems, where the two stars in the binary are white dwarfs, neutron stars, or black holes. A binary star is a Star system consisting of two Stars orbiting around their Center of mass. A white dwarf, also called a degenerate dwarf, is a small Star composed mostly of Electron-degenerate matter. A neutron star is a type of remnant that can result from the Gravitational collapse of a massive Star during a Type II, Type Ib or Type A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e

Although gravitational radiation has not yet been directly detected, it has been indirectly shown to exist. This was the basis for the 1993 Nobel Prize in Physics, awarded for measurements of the Hulse-Taylor binary system. Year 1993 ( MCMXCIII) was a Common year starting on Friday (link will display full 1993 Gregorian calendar) The Nobel Prize in Physics (Nobelpriset i fysik is awarded once a year by the Royal Swedish Academy of Sciences. PSR B1913+16 (also known as J1915+1606 is a Pulsar in a Binary star system, in orbit with another star around a common center of mass

1 Introduction
2 Effects of a passing gravitational wave
3 Sources of gravitational waves
4 Astrophysics and gravitational waves
- 4.1 Energy, momentum, and angular momentum carried by gravitational waves
5 Gravitational wave detectors
- 5.1 Einstein@Home
6 Mathematics
- 6.1 Linear approximation
- 6.2 Relation to the source
7 See also
8 References
9 External links

Introduction

In Einstein's theory of general relativity, the force of gravity is due to curvature of spacetime. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS This curvature is caused by the presence of massive objects. Roughly speaking, the more massive the object is, the greater the curvature it causes, and hence the more intense the gravity. As massive objects move around in spacetime, the curvature will change to reflect the changed locations of those objects. If the objects move around in a certain way, ripples in spacetime can spread outward like ripples on the surface of a pond. These ripples are gravitational waves.

The simplest example of a strong source of gravitational waves is a spinning neutron star with a small mountain on its surface. A neutron star is a type of remnant that can result from the Gravitational collapse of a massive Star during a Type II, Type Ib or Type The mountain's mass will cause curvature of the spacetime. Its movement will "stir up" spacetime, much like a paddle stirring up water. The waves will spread out through the Universe at the speed of light, never stopping or slowing down.

As these waves pass a distant observer, that observer will find spacetime distorted in a very particular way. Distances between objects will increase and decrease rhythmically as the wave passes. The magnitude of this effect will decrease the farther the observer is from the source. Any gravitational waves expected to be seen on Earth will be quite small; the change in size of any object will never be much more than 1 in 10²⁰. Still, scientists are attempting to measure the effects of these waves using extraordinarily precise experiments.

By measuring these waves, astrophysicists hope to learn about systems that they could not observe with more traditional means such as optical telescopes, radio telescopes, etc. An optical telescope is a Telescope which is used to gather and focus light mainly from the visible part of the Electromagnetic spectrum A radio telescope is a form of directional Radio antenna used in Radio astronomy and in tracking and collecting data from Satellites Gravitational waves can penetrate regions that the more familiar waves cannot, providing us with a view of black holes and other mysterious objects in the distant Universe. Using precise measurements of gravitational waves in this way will also allow us to test the general theory of relativity more thoroughly.

In principle, gravitational waves could exist at any frequency. However, very low frequency waves would be impossible to detect, and very high frequency waves have no credible source able to generate detectable waves. Stephen W. Hawking and Werner Israel list different frequency bands for gravitational waves that could be plausibly detected, ranging from 10^-7 Hz up to 10¹¹ Hz. Stephen William Hawking CH, CBE, FRS, FRSA (born 8 January 1942 is a British theoretical physicist. Werner Israel, OC, FRSC, FRS (born October 4, 1931) is a Canadian physicist ^[1]

Effects of a passing gravitational wave

The effect of a plus-polarized gravitational wave on a ring of particles.

The effect of a cross-polarized gravitational wave on a ring of particles.

Imagine a perfectly flat region of spacetime, with a group of motionless test particles lying in a plane. Then, a weak gravitational wave arrives, passing through the particles along a line perpendicular to the plane of the particles. What happens to the test particles? Roughly speaking, they will oscillate in a "cruciform" manner, as shown in the animations. For the resurrection device/parasite at the Hyperion Cantos see Cruciform (Hyperion Cantos. The area enclosed by the test particles does not change, and there is no motion along the direction of propagation. In the animation at the right, the wave would be passing from you, through the screen, and out the back.

The foregoing animation is the result of a pair of masses that orbit about each other (e. g. , black holes) on a circular orbit or a rotating rod or dumbbell. In this case the amplitude, A, of the gravitational wave is a constant, but its plane of polarization changes or rotates (at twice the orbital or rotating-rod rate) and so the time-varying gravitational wave size or periodic spacetime strain h, exhibits a variation as shown in the animation. ^[2] If the orbit is elliptical or the rotating rod’s centrifugal-force change varies during rotation, then the gravitational wave’s amplitude (that is, the amplitude of the periodic spacetime h), A, actually also varies with time according to an equation called the “quadrupole”. ^[3]

Like other waves, there are a few useful numbers describing a gravitational wave:

Amplitude: Usually denoted $h$ , this is the size of the wave — the fraction of stretching or squeezing in the animation. A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. The amplitude shown here is roughly $h = 0. 5$ (or 50%). Gravitational waves passing through the Earth are many billion times weaker than this — $h \approx 10^{-20}$ .
Frequency: Usually denoted $ν$ , this is the frequency with which the wave oscillates (1 divided by the amount of time between maximum stretch or squeeze)
Wavelength: Usually denoted $λ$ , this is the distance along the wave between points of maximum stretch or squeeze.
Speed: This is the speed at which a point on the wave (for example, a point of maximum stretch or squeeze) travels. For gravitational waves with small amplitudes, this is equal to the speed of light, $c$ .

The frequency, wavelength, and speed are related by the equation c = λ ν, just like the equation for a light wave. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. For example, the animations shown here oscillate roughly once every two seconds. This would correspond to a frequency of 0. 5 Hz, and a wavelength of about 600,000 km, or 47 times the diameter of the Earth.

In the example just discussed, we actually assume something special about the wave. We have assumed that the wave is linearly polarized, with a "plus" polarization, written $h_{\,+}$ . In Electrodynamics, linear polarization or plane polarization of Electromagnetic radiation is a confinement of the Electric field vector or Polarization of a gravitational wave is just like polarization of a light wave, except that the polarizations of a gravitational wave are at 45 degrees, as opposed to 90 degrees. In particular, if we had a "cross"-polarized gravitational wave, $h_{\,\times}$ , the effect on the test particles would be basically the same, but rotated by 45 degrees, as shown in the second animation. Just as with light polarization, the polarizations of gravitational waves may also be expressed in terms of circularly polarized waves. In Electrodynamics, circular polarization (also circular polarisation) of Electromagnetic radiation is a Polarization such that the tip of the Gravitational waves are polarized because of the nature of their sources. The polarization of a wave actually depends on the angle from the source, as we will see in the next section.

Sources of gravitational waves

In general terms, gravitational waves are radiated by objects whose motion involves acceleration, provided that the motion is not perfectly spherically symmetric (like a spinning, expanding or contracting sphere) or cylindrically symmetric (like a spinning disk). Symmetry generally conveys two primary meanings The first is an imprecise sense of harmonious or aesthetically-pleasing proportionality and balance such that it reflects beauty or

A simple example is the spinning dumbbell. Set upon one end, so that one side of the dumbell is on the ground and the other end is pointing up, the dumbbell will not radiate when it spins around its vertical axis but will radiate if it tumbles end-over-end. The heavier the dumbbell, and the faster it tumbles, the greater is the gravitational radiation it will give off. If we imagine an extreme case in which the two weights of the dumbbell are massive stars like neutron stars or black holes, orbiting each other quickly, then significant amounts of gravitational radiation would be given off.

Some more detailed examples:

Two objects orbiting each other in a quasi-Keplerian planar orbit (basically, as a planet would orbit the Sun) will radiate.
A spinning non-axisymmetric planetoid — say with a large bump or dimple on the equator — will radiate.
A supernova will radiate except in the unlikely event that it is perfectly symmetric. A supernova (plural supernovae or supernovas) is a stellar Explosion.
An isolated non-spinning solid object moving at a constant speed will not radiate. This can be regarded as a consequence of the principle of conservation of linear momentum. In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product
A spinning disk will not radiate. This can be regarded as a consequence of the principle of conservation of angular momentum. In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position On the other hand, this system will show gravitomagnetic effects. Gravitomagnetism (sometimes Gravitoelectromagnetism, abbreviated GEM) refers to a set of formal analogies between Maxwell's field
A spherically pulsating spherical star (non-zero monopole moment or mass, but zero quadrupole moment) will not radiate, in agreement with Birkhoff's theorem. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object In General relativity, Birkhoff's theorem states that any spherically symmetric solution of the Vacuum field equations must be stationary and

More technically, the second time derivative of the quadrupole moment (or the l-th time derivative of the l-th multipole moment) of an isolated system's stress-energy tensor must be nonzero in order for it to emit gravitational radiation. A quadrupole or quadrapole is one of a sequence of configurations of — for example — electric charge or current or gravitational mass that can exist in ideal form but it A multipole expansion is a mathematical series representing a function that depends on angles — usually the two angles on a sphere. The stress-energy tensor (sometimes stress-energy-momentum tensor is a Tensor quantity in Physics that describes the Density and Flux This is analogous to the changing dipole moment of charge or current necessary for electromagnetic radiation.

Power radiated by the Earth-Sun system

We imagine a simple system of two masses — such as the Earth-Sun system — moving slowly compared to the speed of light. Assume that these two masses orbit each other in a circular orbit in the $x$ - $y$ plane. To a good approximation, the masses follow simple Keplerian orbits. In Physics, an orbit is the gravitationally curved path of one object around a point or another body for example the gravitational orbit of a planet around a star However, such an orbit represents a changing quadrupole moment. That is, the system will give off gravitational waves.

Suppose that the two masses are $M 1$ and $M 2$ , and they are separated by a distance $R$ . The power given off (radiated) by this system is

$P = \frac{dE}{dt} = \frac{32}{5} \frac{G^4}{c^5}\, \frac{(M_1M_2)^2 (M_1+M_2)}{R^5}\, \approx 2^7 \frac{M_1}{M_2} \left(\frac{v}{c}\right)^5 \frac{E_{kin,1}}{T} \, ,$

where G is the Gravitational Constant and $E k i n,1$ , T and v are the kinetic energy, the period time and velocity of the first mass. The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass This is derived from Einstein's quadrupole equation. ^[2] For a system like the Earth and the Sun, $R$ is very large (about 1. 5×10¹¹ m) and $M 1$ and $M 2$ are relatively very small (about 2×10³⁰ and 6×10²⁴ kg respectively). Substituting these values into the above equation gives about 313 watts of power radiated by the Earth-Sun system in the form of gravitational waves.

Wave amplitudes from the Earth-Sun system

We can also think in terms of the amplitude of the wave. Suppose that an observer is positioned at a distance $r$ from the center of mass of the system, at spherical coordinates $(r,θ,φ)$ . In Mathematics, the spherical coordinate system is a Coordinate system for representing geometric figures in three dimensions using three coordinates the radial If the observer is well outside the system (in fact, we need $r > c / Ω$ ), the two polarizations of the wave will be

$h_{+} = -\frac{1}{r}\, \frac{G^2}{c^4}\, \frac{2 M_1 M_2}{R} (1+\cos^2\theta) \cos\left[2\Omega (t - r) - 2\phi\right]\ ,$

$h_{\times} = -\frac{1}{r}\, \frac{G^2}{c^4}\, \frac{4 M_1 M_2}{R}\, \cos{\theta} \sin \left[2 \Omega (t - r) - 2\phi \right]\ .$

Here, we use the constant angular velocity $\Omega=\sqrt{G(M_1+M_2)/R^3}$ of a circular orbit in Newtonian physics. Do not confuse with Angular frequency The unit for angular velocity is rad/s Note that the polarization depends on the angle to the system. For example, if the observer is in the $x$ - $y$ plane then $θ = π / 2$ , and $cosθ = 0$ , so the $h_\times$ polarization is always zero. We also see that the frequency of the wave given off is $ν = 2Ω / 2π = Ω / π$ . If we put in numbers for the Earth-Sun system, we find

$-\frac{1}{r}\, \frac{G^2}{c^4}\, \frac{4M_1 M_2}{R} = -\frac{1}{r}\, 1.7\times 10^{-10}\, \mathrm{meters}\ .$

In this case, the minimum distance to find waves is $r = c/\Omega \approx 1$ light year, so typical amplitudes will be $h \approx 10^{-26}$ . A light-year or light year (symbol ly) is a unit of Length, equal to just under ten trillion Kilometres As defined by That is, a ring of particles would stretch or squeeze by just $10 - 24$ percent.

Radiation from other sources

Although the waves from the Earth-Sun system are minuscule, astronomers can point to other sources for which the radiation should be substantial. One important example is the Hulse-Taylor binary — a pair of stars, one of which is a pulsar. PSR B1913+16 (also known as J1915+1606 is a Pulsar in a Binary star system, in orbit with another star around a common center of mass Pulsars are highly magnetized rotating Neutron stars that emit a beam of Electromagnetic radiation in the form of radio waves The characteristics of their orbit can be deduced from the Doppler shifting of radio signals given off by the pulsar. The Doppler effect (or Doppler shift) named after Christian Doppler, is the change in Frequency and Wavelength of a Wave for Each of the stars has a mass about 1. 4 times that of the Sun. Also, their orbit is about one seventy-fifth the distance between the Earth and Sun — which means the distance between the two stars is just a few times larger than the diameter of our own Sun. This combination of greater masses and smaller separation means that the energy given off by the Hulse-Taylor binary will be far greater than the energy given off by the Earth-Sun system — roughly $1022$ times as much.

The information about the orbit can be used to predict just how much energy (and angular momentum) should be given off in the form of gravitational waves. As the energy is carried off, the orbit will change; the stars will draw closer to each other. This effect of drawing closer is called an inspiral, and it can be observed in the pulsar's signals. The measurements on this system were carried out over several decades, and it was shown that the changes predicted by gravitational radiation in general relativity matched the observations very well. In 1993, Russell Hulse and Joe Taylor were awarded the Nobel Prize in Physics for this observation which was the first observational evidence for gravitational waves. Year 1993 ( MCMXCIII) was a Common year starting on Friday (link will display full 1993 Gregorian calendar) Russell Alan Hulse (born November 28, 1950) is an American Physicist and winner of the Nobel Prize in Physics, shared with his Joseph Hooton Taylor Jr (born March 29, 1941) is an American Astrophysicist and Nobel Prize in Physics laureate The Nobel Prize in Physics (Nobelpriset i fysik is awarded once a year by the Royal Swedish Academy of Sciences.

Inspirals are very important sources of gravitational waves. Any time two compact objects (white dwarfs, neutron stars, or black holes) come close to each other, they send out intense gravitational waves. As the objects come closer and closer to each other (that is, as $R$ becomes smaller and smaller), the gravitational waves become more and more intense. At some point these waves should become so intense that they can be directly detected by their effect on objects on the Earth. This direct detection is the goal of several large experiments around the world.

The only difficulty is that systems like the Hulse-Taylor binary are so far away. The amplitude of waves given off by the Hulse-Taylor binary as seen on Earth would be roughly $h \approx 10^{-26}$ . There are some sources, however, that astrophysicists expect to find with the somewhat larger amplitudes of $h \approx 10^{-20}$ .

Astrophysics and gravitational waves

Unsolved problems in physics: Is our universe filled with gravitational radiation from the big bang? From astrophysical sources, such as inspiraling neutron stars? What can this tell us about quantum gravity and general relativity?

During the past century, astronomy has been revolutionized by the use of new methods for observing the universe. This is a list of some of the major unsolved problems in Physics. A neutron star is a type of remnant that can result from the Gravitational collapse of a massive Star during a Type II, Type Ib or Type Quantum gravity is the field of Theoretical physics attempting to unify Quantum mechanics, which describes three of the fundamental forces of nature Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study Astronomical observations were originally made using visible light. Galileo Galilei pioneered the use of telescopes to enhance these observations. Galileo Galilei (15 February 1564 &ndash 8 January 1642 was a Tuscan ( Italian) Physicist, Mathematician, Astronomer, and Philosopher However, visible light is only a small portion of the electromagnetic spectrum, and not all objects in the distant universe shine strongly in this particular band. The electromagnetic (EM spectrum is the range of all possible Electromagnetic radiation frequencies More useful information may be found, for example, in radio wavelengths. Using radio telescopes, astronomers have found pulsars, quasars, and other extreme objects which push the limits of our understanding of physics. A radio telescope is a form of directional Radio antenna used in Radio astronomy and in tracking and collecting data from Satellites Pulsars are highly magnetized rotating Neutron stars that emit a beam of Electromagnetic radiation in the form of radio waves A quasar (contraction of QUASi-stellAR radio source) is an extremely powerful and distant Active galactic nucleus. Observations in the microwave band have opened our eyes to the faint imprints of the Big Bang a discovery Stephen Hawking called the "greatest discovery of the century, if not all time". Microwaves are electromagnetic waves with Wavelengths ranging from 1 mm to 1 m or frequencies between 0 The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation. Stephen William Hawking CH, CBE, FRS, FRSA (born 8 January 1942 is a British theoretical physicist. Similar advances in observations using gamma rays, x-rays, ultraviolet light, and infrared light have also brought new insights to astronomy. Gamma rays (denoted as &gamma) are a form of Electromagnetic radiation or light emission of frequencies produced by sub-atomic particle interactions X-radiation (composed of X-rays) is a form of Electromagnetic radiation. Ultraviolet ( UV) light is Electromagnetic radiation with a Wavelength shorter than that of Visible light, but longer than X-rays Infrared ( IR) radiation is Electromagnetic radiation whose Wavelength is longer than that of Visible light, but shorter than that of As each of these regions of the spectrum has opened, new discoveries have been made that could not have been made otherwise. Astronomers hope that the same holds true of gravitational waves.

Gravitational waves have two important and unique properties. First, there is no need for any type of matter to be present nearby in order for the waves to be generated by a binary system of uncharged black holes, which would emit no electromagnetic radiation. Second, gravitational waves can pass through any intervening matter without being scattered. Whereas light from distant stars may be blocked out by interstellar dust, for example, gravitational waves will pass through unimpeded. These two features allow gravitational waves to carry information about astronomical phenomena never before observed by humans.

The sources of gravitational waves described above are in the low-frequency end of the gravitational-wave spectrum (10^-7 to 10⁵ Hz). An astrophysical source at the high-frequency end of the gravitational-wave spectrum (above 10⁵ Hz and probably 10¹⁰ Hz) generates relic gravitational waves that are theorized to be faint imprints of the Big Bang like the cosmic microwave background. ^[4] At these high frequencies it is potentially possible that the sources may be “man made”^[1] that is, gravitational waves generated and detected in the laboratory. ^[5]^[6]

Energy, momentum, and angular momentum carried by gravitational waves

Waves familiar from other areas of physics such as water waves, sound waves, and electromagnetic waves are able to carry energy, momentum, and angular momentum. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position By carrying these away from a source, waves are able to rob that source of its energy, linear or angular momentum. Gravitational waves perform the same function. Thus for example a binary system loses angular momentum as the two orbiting objects spiral towards each other - the angular momentum is radiated away by gravitational waves. The waves can also carry off linear momentum, a possibility that has some interesting implications for Astrophysics. Astrophysics is the branch of Astronomy that deals with the Physics of the Universe, including the physical properties ( Luminosity, Consider for instance a cluster of stars with a binary black hole system in the center. The holes orbit each other, but their center of mass doesn't move with respect to the cluster at first. However, as the binary inspirals, the radiated gravitational waves carry away linear momentum in some direction. In keeping with Newton's third law of motion, the binary will gain some linear momentum in the opposite direction. Newton's laws of motion are three Physical laws which provide relationships between the Forces acting on a body and the motion of the Thus, it may be shot out of the cluster.

Gravitational wave detectors

Though the Hulse-Taylor observations were very important, they were only indirect evidence for gravitational waves. A more interesting observation would be a direct measurement of the effect of a passing gravitational wave. Not only would a direct measurement of gravitational waves rule out other possible (however unlikely) reasons for changes to the orbit of an inspiraling system, it would also provide us more information on the system. Perhaps more importantly, such a detection could give us information about things we can't see with radio or light waves — such as black holes. A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e This would provide us with a rigorous test for Einstein's theory of general relativity. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916

The great challenge of this type of detection, though, is the extraordinarily small effect the waves would produce on a detector. The amplitude of any wave will fall off as the inverse of the distance from the source (the $1 / r$ term in the formulas for $h$ above). Thus, even waves from extreme systems like merging binary black holes die out to very small amplitude by the time they reach the Earth. Astrophysicists expect that some gravitational waves passing the Earth may be as large $h\approx 10^{-20}$ , but generally no bigger. For an object 1 meter in length, this means that its ends would move by $10 - 20$ meters relative to each other. This distance is about 1 billionth of the width of a typical atom, and roughly one one-hundred-thousandth the width of a proton. History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive

A simple device to detect this motion is called a Weber bar — a large, solid piece of metal with electronics attached to detect any vibrations. A Weber bar is a device used in the detection of gravitational waves first devised and constructed by Physicist Joseph Weber at the University of Maryland This type of instrument was the first type of gravitational wave detector. The idea is to wait for a passing gravitational wave to "ring up" a bar at its resonant frequency, which would basically amplify the wave naturally. In Physics, resonance is the tendency of a system to Oscillate at maximum Amplitude at certain frequencies, known as the system's Alternatively, a nearby supernova might be strong enough to be seen without resonant amplification. Modern forms of the Weber bar are still operated, cryogenically cooled, with superconducting quantum interference devices to detect the motion. Cryogenics is often used incorrectly to refer to Cryonics, cryopreserving humans or animals Squid are marine Cephalopods of the order Teuthida, which comprises around 300 species Unfortunately, Weber bars are not sensitive enough to detect anything but extremely powerful gravitational waves. ^[7]

A schematic diagram of a laser interferometer.

A more sensitive version is the laser interferometer, with separate masses placed many hundreds of meters to several kilometers apart acting as two ends of a bar. Interferometry is the technique of using the pattern of Interference created by the superposition of two or more Waves to diagnose the properties of Ground-based interferometers are now operating, and taking data. Currently, the most sensitive is LIGO — the Laser Interferometer Gravitational Wave Observatory. For the Latvian holiday Ligo see Jāņi. LIGO stands for Laser Interferometer Gravitational-Wave Observatory. This is actually a set of three devices: one in Livingston, Louisiana; the other two (in the same vacuum tubes) at the Hanford site in Richland, Washington. Livingston is a town in and the Parish seat of Livingston Parish, Louisiana, United States. The Hanford Site is a decommissioned nuclear production complex on the Columbia River in south-central Washington operated by the United States government Richland is a city in Benton County in the southeastern part of the U Each consists of two light storage arms which are 2 to 4 kilometers in length. These are at 90 degree angles to each other, and consist of large vacuum tubes running the entire 4 kilometers. A passing gravitational wave will then slightly stretch one arm as it shortens the other. This is precisely the motion to which an interferometer is most sensitive.

Even with such long arms, a gravitational wave will only change the distance between the ends of the arms by about $10 - 17$ meters at most. This is still only a fraction of the width of a proton. Nonetheless, LIGO's interferometers are now running routinely at an even better sensitivity level. LIGO's should be able to detect gravitational waves as small as $h \approx 5\times 10^{-22}$ , but needs to wait until a gravitational wave with at least that amplitude passes. Upgrades to LIGO and other detectors such as VIRGO, GEO, and TAMA 300 should increase the sensitivity still further — by a factor of up to 100. The Virgo detector for Gravitational waves consists mainly in a Michelson Laser Interferometer made of two orthogonal arms being each 3 kilometers TAMA 300 is a Gravitational wave detector located at the Mitaka campus of the National Astronomical Observatory of Japan. Another highly sensitive interferometer (LCGT) is currently in the design phase. The Large Scale Cryogenic Gravitational Wave Telescope (LCGT is a future project of the Gravitational wave studies group at the Institute for Cosmic Ray Research

All detectors are limited at high frequencies by shot noise, which occurs because the lasers cannot produce photons at an absolutely constant rate. Shot noise is a type of Electronic noise that occurs when the finite number of particles that carry energy such as Electrons in an electronic circuit or Photons Since there may not be a normal number of photons arriving in a given time interval (for instance in such cases as the laser being momentarily not intense enough), it will be impossible to tell whether a measurement is due to real data, or just random fluctuations in the number of photons. The more independent detectors produce equivalent measurements for any given time period, the more certain experimenters can be that they are getting valid results, i. e. , results not influenced by momentary lags in production of photons by a given laser.

All ground-based detectors are also limited at low frequencies by seismic noise, and must be very well isolated from seismic disturbances. Seismology (from Greek grc σεισμός seismos, "earthquake" and grc -λογία -logia) is the scientific study of Earthquakes Passing cars and trains, falling trees, earthquakes, and even waves crashing on the shore hundreds of miles away are all very significant sources of noise in real interferometers.

Space-based interferometers, such as LISA, are also being developed. The Laser Interferometer Space Antenna (LISA experiment is a joint venture of NASA and the European Space Agency (ESA to detect and observe in detail Gravitational LISA's design calls for test masses to be placed five million kilometers apart, in separate spacecraft, with lasers running between them. Because of the distance between the spacecraft, it will be impossible to create light storage arms. Also, the arms will be at 60 degree angles to each other, rather than 90 degree angles. Still, the principle will be the same. Although LISA will not be affected by seismic noise, it will be affected by other noise sources, including noise from cosmic rays and solar wind and — of course — shot noise. For the 1962 Bruce Conner film see Cosmic Ray (film Cosmic rays are energetic particles originating from space that impinge on The solar wind is a Stream of charged particles&mdasha plasma &mdashthat are ejected from the upper atmosphere of the Sun.

There are other prospects such as MiniGRAIL, a spherical gravitational wave antenna based at Leiden University. MiniGRAIL is the world's first spherical Gravitational wave detector based at Leiden University, the Netherlands. Leiden University (Universiteit Leiden located in the city of Leiden, is the oldest University in The Netherlands. Some scientists even want to use the moon as a giant gravitational wave detector. The moon should be somewhat pliable to the contortions caused by gravitational waves, and the hope is that the motion of the moon caused by these waves will be detectable, much like the motion of a Weber bar. A Weber bar is a device used in the detection of gravitational waves first devised and constructed by Physicist Joseph Weber at the University of Maryland

The detectors of gravitational waves described in the foregoing are in the low-frequency end of the gravitational-wave spectrum (10^-7 to 10⁵ Hz). There are currently two fabricated high-frequency gravitational wave (HFGW) detectors: one at Birmingham University, England and the other at INFN Genoa, Italy. In addition there are some under development at Chongqing University, China. The Birmingham HFGW high-frequency gravitational wave detector measures changes in the polarization state of a microwave beam (caused by the presence of a gravitational wave or GW) circulating in a closed loop about one meter across. Microwaves are electromagnetic waves with Wavelengths ranging from 1 mm to 1 m or frequencies between 0 Two have been fabricated and they are currently expected to be sensitive to HFGWs having periodic spacetime strains of $h\sim{2 \times 10^{-13}/\sqrt{\mathit{Hz}}}$ , given as an amplitude spectral density. In Statistical signal processing and Physics, the spectral density, power spectral density ( PSD) or energy spectral density ( The INFN Genoa detector, or resonant antenna, consists of two coupled, superconducting, spherical, harmonic oscillators a few centimeters in diameter. Superconductivity is a phenomenon occurring in certain Materials generally at very low Temperatures characterized by exactly zero electrical resistance The oscillators are designed to have (when uncoupled) almost equal resonant frequencies. In theory the system is currently expected to have a sensitivity to HFGWs having periodic spacetime strains of $h\sim{2 \times 10^{-17}/\sqrt{\mathit{Hz}}}$ with an expectation to reach a sensitivity of $h\sim{2 \times 10^{-20}/\sqrt{\mathit{Hz}}}$ .

The Chongqing University detectors are based upon the GW theory first put forth by Gertsenshtein in 1962. These Chinese detectors aim at the selection and detection of relic high-frequency gravitational waves with the predicted typical parameters ν_g ~ 10¹⁰ Hz (10 GHz) and h ~ 10^-30-10^-31. The usual Gertsenshtein effect^[8] involves the generation of gravitational waves by electromagnetic waves under the influence of a strong static magnetic field. In this case the gravitational waves produced will have the same frequency as the electromagnetic waves producing them. The inverse Gertsenshtein effect, which is alluded to at the end of the paper involves what is termed a synchro-resonance condition. Thus in the Chinese detectors a strong electromagnetic beam (essentially a focused microwave, so called “Gaussian beam”) at the expected frequency, phase and bandwidth of the relic gravitational waves is passed through a strong static magnetic field. In Optics, a Gaussian beam is a Beam of Electromagnetic radiation whose transverse Electric field and Intensity ( Irradiance There are then produced electromagnetic “detection” photons due to the gravitational waves. These detection photons move off at right angles to the electromagnetic beam and to the direction of the magnetic field. According to theory they move off in both directions and the experimental plan is that they be intercepted by two very sensitive microwave receivers or detectors. Noise is suppressed by keeping the detector at very low temperature (less than 0. 048 K) and including superconductor interior baffles and a superconductor enclosure called a “Faraday Cage,” both composed of a mosaic of high-temperature superconductor tiles (e. A Faraday cage or Faraday shield is an enclosure formed by conducting material, or by a mesh of such material High-temperature superconductors (abbreviated high Tc or HTS) are a family of superconducting Ceramic materials largely g. , YBCO). Yttrium barium copper oxide, often abbreviated YBCO is a Chemical compound with the formula Y[[Barium Ba]]2 Cu 3 O 7 Similar to the Advanced LIGO, LISA, et al. detectors, these Chinese detectors are in the design phase.

Einstein@Home

Main article: Einstein@Home

In some sense, the easiest signals to detect should be constant sources. Einstein@Home is a Distributed computing project hosted by the University of Wisconsin-Milwaukee and running on the Berkeley Open Infrastructure for Network Computing Supernovae and neutron star or black hole mergers should have larger amplitudes and be more interesting, but their waves will be more complicated. The waves given off by a spinning, bumpy neutron star would be "monochromatic" — like a pure tone in acoustics. Monochrome comes from the Greek μονόχρωμος ( monochromos) meaning “of one color” which is a combination A pure tone is a tone with a sinusoidal waveshape A Sine wave is characterized by its frequency — the number of cycles per second or its Wavelength Acoustics is the interdisciplinary science that deals with the study of Sound, Ultrasound and Infrasound (all mechanical waves in gases liquids and solids It would not change very much in amplitude or frequency.

The Einstein@Home project is a distributed computing project similar to SETI@home intended to detect this type of simple gravitational wave. Einstein@Home is a Distributed computing project hosted by the University of Wisconsin-Milwaukee and running on the Berkeley Open Infrastructure for Network Computing Distributed computing deals with Hardware and Software Systems containing more than one processing element or Storage element concurrent SETI@home ("SETI at home" is a Distributed computing ( Grid computing) project using Internet -connected computers hosted by the Space By taking data from LIGO and GEO, and sending it out in little pieces to thousands of volunteers for analysis on their home computers, Einstein@Home can sift through the data far more quickly than would be possible otherwise. Searches for gravitational waves from other types of systems require large supercomputers running for long periods.

A simple computer program can be downloaded to any home computer, and acts as a screen saver to use computer time that would otherwise be wasted. The program automatically downloads the data, analyzes it while the screen saver is running, and sends the final results back to a central computer. ^[9]

Mathematics

Einstein's equations form the fundamental law of general relativity. The Einstein field equations ( EFE) or Einstein's equations are a set of ten equations in Einstein 's theory of General relativity in which the The curvature of spacetime can be expressed mathematically using the metric tensor — denoted $g μν$ . In the mathematical field of Differential geometry, a metric tensor is a type of function defined on a Manifold (such as a Surface in space The metric holds information regarding how distances are measured in the space under consideration. Because the propagation of gravitational waves through space and time change distances, we will need to use this to find the solution to the wave equation.

Spacetime curvature is also expressed with respect to a covariant derivative, $\nabla$ , in the form of the Einstein tensor — $G μν$ . In Mathematics, the covariant derivative is a way of specifying a Derivative along Tangent vectors of a Manifold. The Einstein tensor expresses Spacetime curvature in the Einstein field equations for Gravitation in the Theory of general relativity. This curvature is related to the stress-energy tensor — $T μν$ — by the key equation

$G_{\mu \nu} = \frac{8\pi G_N}{c^4} T_{\mu \nu}\ ,$

where $G N$ is Newton's gravitational constant, and $c$ is the speed of light. The stress-energy tensor (sometimes stress-energy-momentum tensor is a Tensor quantity in Physics that describes the Density and Flux The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass We assume geometrized units, so $G N = 1 = c$ . A geometrized unit system or geometric unit system is a system of Natural units in which the base physical units are chosen so that the Speed of light

With some simple assumptions, Einstein's equations can be rewritten to show explicitly that they are just wave equations. The wave equation is an important second-order linear Partial differential equation that describes the propagation of a variety of Waves such as Sound waves To begin with, we adopt some coordinate system, like $(t, r,θ,φ)$ . We define the "flat-space metric" $η μν$ to be the quantity which — in this coordinate system — has the components we would expect for the flat space metric. For example, in these spherical coordinates, we have

$\eta_{\mu \nu} = \begin{bmatrix} -1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & r^2 & 0 \\ 0 & 0 & 0 & r^2 \sin^2\theta \end{bmatrix}\ .$

This flat-space metric has no physical significance; it is a purely mathematical device necessary for the analysis. Tensor indices are raised and lowered using this "flat-space metric".

Now, we can also think of the physical metric $g μν$ as a matrix, and find its determinant, $\det\ g$ . In Mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries) which may be Numbers or more generally In Algebra, a determinant is a function depending on n that associates a scalar, det( A) to every n × n Finally, we define a quantity

$\bar{h}^{\alpha \beta} \equiv \eta^{\alpha \beta} - \sqrt{|\det g|} g^{\alpha \beta}\ .$

This is the crucial field, which will represent the radiation. It is possible (at least in an asymptotically flat spacetime) to choose the coordinates in such a way that this quantity satisfies the "de Donder" gauge conditions (conditions on the coordinates):

$\nabla_\beta\, \bar{h}^{\alpha \beta} = 0\ ,$

where $\nabla$ represents the flat-space derivative operator. An asymptotically flat spacetime is a Lorentzian manifold in which roughly speaking the curvature vanishes at large distances from some region so that at large distances These equations say that the divergence of the field is zero. In Vector calculus, the divergence is an Operator that measures the magnitude of a Vector field &rsquos source or sink at a given point the The full, nonlinear Einstein equations can now be written^[10] as

$\Box \bar{h}^{\alpha \beta} = -16\pi \tau^{\alpha \beta}\ ,$

where $\Box = -\partial_t^2 + \Delta$ represents the flat-space d'Alembertian operator, and $τ αβ$ represents the stress-energy tensor plus quadratic terms involving $\bar{h}^{\alpha \beta}$ . In Special relativity, Electromagnetism and wave theory, the d'Alembert operator \Box also called the d'Alembertian or the This is just a wave equation for the field with a source, despite the fact that the source involves terms quadratic in the field itself. That is, it can be shown that solutions to this equation are waves traveling with velocity 1 in these coordinates.

Linear approximation

The equations above are valid everywhere — near a black hole, for instance. However, because of the complicated source term, the solution is generally too difficult to find analytically. We can often assume that space is nearly flat, so the metric is nearly equal to the $η αβ$ tensor. In this case, we can neglect terms quadratic in $\bar{h}^{\alpha \beta}$ , which means that the $τ αβ$ field reduces to the usual stress-energy tensor $T αβ$ . That is, Einstein's equations become

$\Box \bar{h}^{\alpha \beta} = -16\pi T^{\alpha \beta}\ .$

If we are interested in the field far from a source, however, we can treat the source as a point source; everywhere else, the stress-energy tensor would be zero, so

$\Box \bar{h}^{\alpha \beta} = 0\ .$

Now, this is the usual homogeneous wave equation — one for each component of $\bar{h}^{\alpha \beta}$ . Solutions to this equation are well known. For a wave moving away from a point source, the radiated part (meaning the part that dies off as $1 / r$ far from the source) can always be written in the form $A (t - r,θ,φ) / r$ , where $A$ is just some function. It can be shown^[11] that — to a linear approximation — it is always possible to make the field traceless. Now, if we further assume that the source is positioned at $r = 0$ , the general solution to the wave equation in spherical coordinates is

$\begin{array}{lcl} \bar{h}^{\alpha \beta} & = & \frac{1}{r}\, \begin{bmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & A_{+}(t-r,\theta,\phi) & A_{\times}(t-r,\theta,\phi) \\ 0 & 0 & A_{\times}(t-r,\theta,\phi) & -A_{+}(t-r,\theta,\phi) \end{bmatrix} \\ \\ & \equiv & \begin{bmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & h_{+}(t-r,r,\theta,\phi) & h_{\times}(t-r,r,\theta,\phi) \\ 0 & 0 & h_{\times}(t-r,r,\theta,\phi) & -h_{+}(t-r,r,\theta,\phi) \end{bmatrix} \end{array}$

where we now see the origin of the two polarizations.

Relation to the source

If we know the details of a source — for instance, the parameters of the orbit of a binary — we can relate the source's motion to the gravitational radiation observed far away. With the relation

$\Box \bar{h}^{\alpha \beta} = -16\pi \tau^{\alpha \beta}\ ,$

we can write the solution in terms of the tensorial Green's function for the d'Alembertian operator:^[10]

$\bar{h}^{\alpha \beta} (t,\vec{x}) = -16\pi \int\, G^{\alpha \beta}_{\gamma \delta} (t,\vec{x};t',\vec{x}')\, \tau^{\gamma \delta}(t',\vec{x}')\, dt'\, d^3x'\ .$

Though it is possible to expand the Green's function in tensor spherical harmonics, it is easier to simply use the form

$G^{\alpha \beta}_{\gamma \delta} (t,\vec{x};t',\vec{x}') = \frac{1}{4\pi} \delta_{\gamma}^\alpha\, \delta_{\delta}^\beta\, \frac{\delta(t\pm|\vec{x}-\vec{x}'|-t')} {|\vec{x}-\vec{x}'|}\ ,$

where the positive and negative signs correspond to ingoing and outgoing solutions, respectively. In Mathematics, Green's function is a type of function used to solve inhomogeneous Differential equations subject to boundary conditions In Mathematics, the spherical harmonics are the angular portion of an Orthogonal set of solutions to Laplace's equation represented in a system of Generally, we are interested in the outgoing solutions, so

$\bar{h}^{\alpha \beta} (t,\vec{x}) = -4 \int\, \frac{\tau^{\alpha \beta}(t-|\vec{x}-\vec{x}'|,\vec{x}')}{|\vec{x}-\vec{x}'|}\, d^3x'\ .$

If the source is confined to a small region very far away, to an excellent approximation we have:

$\bar{h}^{\alpha \beta} (t,\vec{x}) \approx -\frac{4}{r}\, \int\, \tau^{\alpha \beta}(t-r,\vec{x}')\, d^3x'\ ,$

where $r=|\vec{x}|$ .

Now, because we will eventually only be interested in the spatial components of this equation (time components can be set to zero with a coordinate transformation), and we are integrating this quantity — presumably over a region of which there is no boundary — we can put this in a different form. Ignoring divergences with the help of Stokes' theorem and an empty boundary, we can see that

$\int\, \tau^{i j}(t-r,\vec{x}')\, d^3x' = \int\, x'^i x'^j \nabla_k \nabla_l \tau^{k l} (t-r,\vec{x}')\, d^3x'\ ,$

Inserting this into the above equation, we arrive at

$\bar{h}^{i j} (t,\vec{x}) \approx -\frac{4}{r}\, \int\, x'^i x'^j \nabla_k \nabla_l \tau^{k l} (t-r,\vec{x}')\, d^3x'\ ,$

Finally, because we have chosen to work in coordinates for which $\nabla_\beta\, \bar{h}^{\alpha \beta} = 0$ , we know that $\nabla_\beta\, \tau^{\alpha \beta} = 0$ . In Differential geometry, Stokes' theorem is a statement about the integration of Differential forms which generalizes several Theorems from With a few simple manipulations, we can use this to prove that

$\nabla_0 \nabla_0 \tau^{00} = \nabla_j \nabla_k \tau^{jk}\ .$

With this relation, the expression for the radiated field is

$\bar{h}^{i j} (t,\vec{x}) \approx -\frac{4}{r}\, \frac{d^2}{dt^2}\, \int\, x'^i x'^j \tau^{0 0} (t-r,\vec{x}')\, d^3x'\ .$

In the linear case, $τ 00 = ρ$ , the density of mass-energy.

To a very good approximation, the density of a simple binary can be described by a pair of delta-functions, which eliminates the integral. Explicitly, if the masses of the two objects are $M 1$ and $M 2$ , and the positions are $\vec{x}_1$ and $\vec{x}_2$ , then

$\rho(t-r,\vec{x}') = M_1 \delta^3(\vec{x}'-\vec{x}_1(t-r)) + M_2 \delta^3(\vec{x}'-\vec{x}_2(t-r))\ .$

We can use this expression to do the integral above:

$\bar{h}^{i j} (t,\vec{x}) \approx -\frac{4}{r}\, \frac{d^2}{dt^2}\, \left\{ M_1 x_1^i(t-r) x_1^j(t-r) + M_2 x_2^i(t-r) x_2^j(t-r) \right\}\ .$

Using mass-centered coordinates, and assuming a circular binary, this is

$\bar{h}^{i j} (t,\vec{x}) \approx -\frac{4}{r}\, \frac{M_1 M_2}{R}\, n^i(t-r) n^j(t-r)\ ,$

where $\vec{n} = \vec{x}_1 / |\vec{x}_1|$ . Plugging in the known values of $\vec{x}_1(t-r)$ , we obtain the expressions given above for the radiation from a simple binary.

References

^ ^a ^b Hawking, S. Hawking radiation (also known as Bekenstein-Hawking radiation) is a Thermal radiation with a black body spectrum predicted to be emitted by Black holes W. and Israel, W. , General Relativity: An Einstein Centenary Survey, Cambridge University Press, Cambridge, 1979, 98.
^ ^a ^b Landau, L. D. and Lifshitz, E. M. , The Classical Theory of Fields. Fourth Revised English Edition, Pergamon Press. , 1975, 356-357.
^ Einstein, A. , “The quadrupole formula. ” Sitzungsberichte, Preussische Akademie der Wisserschaften, 154, (1918).
^ L. P. Grishchuk (1976), “Primordial Gravitons and the Possibility of Their Observation,” Sov. Phys. JETP Lett. 23, p. 293.
^ Braginsky, V. B. , Rudenko and Valentin, N. Section 7: “Generation of gravitational waves in the laboratory,” Physics Report (Review section of Physics Letters), 46, No. 5. 165-200, (1978).
^ Li, Fangyu, Baker, R. M L, Jr. , and Woods, R. C. , “Piezoelectric-Crystal-Resonator High-Frequency Gravitational Wave Generation and Synchro-Resonance Detection,” in the proceedings of Space Technology and Applications International Forum (STAIF-2006), edited by M. S. El-Genk, American Institute of Physics Conference Proceedings, Melville NY 813: 2006.
^ For a review of early experiments using Weber bars, see Levine, J. (April 2004). "Early Gravity-Wave Detection Experiments, 1960-1975". Physics in Perspective (Birkhäuser Basel) 6 (1): 42–75. doi:10.1007/s00016-003-0179-6. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.
^ Gertsenshtein, M. E. , “Wave resonance of light and gravitational waves,” Soviet Physics JETP, 14, No. 1, 84-85, (1962).
^ Einstein@Home
^ ^a ^b Thorne, Kip (April 1980). "Multipole expansions of gravitational radiation". Reviews of Modern Physics 52.
^ C. W. Misner, K. S. Thorne, and J. A. Wheeler (1973). Gravitation. W. H. Freeman and Co. .

Chakrabarty, Indrajit, "Gravitational Waves: An Introduction". arXiv:physics/9908041 v1, Aug 21, 1999.
Landau, L. D. and Lifshitz, E. M. , The Classical Theory of Fields (Pergamon Press),(1987).
Will, Clifford M. , The Confrontation between General Relativity and Experiment. Living Rev. Relativity 9 (2006) 3.

External links

Caltech's Physics 237-2002 Gravitational Waves by Kip Thorne Video plus notes: Graduate level but does not assume knowledge of General Relativity, Tensor Analysis, or Differential Geometry; Part 1: Theory (10 lectures), Part 2: Detection (9 lectures)
www.astronomycast.com January 14th, 2008 Episode 71: Gravitational Waves
GraveWave Home Page - Information and a literature survey of high-frequency gravitational waves.
Laser Interferometer Gravitational Wave Observatory. LIGO Laboratory, California Institute of Technology. The California Institute of Technology (commonly referred to as Caltech) is a private, Coeducational research university located in Pasadena
Einstein's Messengers - The LIGO Movie by NSF
Home page for Einstein@Home project, a distributed computing project processing raw data from LIGO Laboratory, searching for gravity waves
The National Center for Supercomputing Applications -- a numerical relativity group
Caltech Relativity Tutorial -- A basic introduction to gravitational waves, and astrophysical systems giving off gravitational waves
Resource Letter GrW-1: Gravitational waves -- a list of books, journals and web resources compiled by Joan Centrella for research into gravitational waves
Mathematical and Physical Perspectives on Gravitational Radiation -- written by B F Schutz of the Max Planck Institute explaining the significance and background of some key concepts in gravitational radiation
Binary BH Merger -- estimating the radiated power and merger time of a BH binary using dimensional analysis

The Max-Planck-Gesellschaft zur Förderung der Wissenschaften e

Dictionary

-noun

(physics) A postulated fluctuation in spacetime that propagates as a wave at the speed of light

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