Gravitomagnetism

This article is about the gravitational analog of electromagnetism as a whole. For specifically the gravitational analog of magnetism, see frame-dragging. Albert Einstein 's theory of General relativity predicts that rotating bodies drag Spacetime around themselves in a phenomenon referred to as frame-dragging

Gravitomagnetism (sometimes Gravitoelectromagnetism, abbreviated GEM), refers to a set of formal analogies between Maxwell's field equations and an approximation to the Einstein field equations for general relativity, valid under certain conditions. Analogy is both the cognitive process of transferring Information from a particular subject (the analogue or source to another particular subject (the target and In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric 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 or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 For instance, the most common version of GEM is valid only far from isolated sources, and for slowly moving test particles. In physical theories, a test particle is an idealized model of an object whose physical properties (usually Mass, Charge, or size) are assumed

1 Background
2 Equations
- 2.1 Comparison with electromagnetism
3 Higher-order effects
4 Gravitomagnetic field of Earth
5 Fringe physics
6 References
7 See also
8 External links

Background

This approximate reformulation of gravitation as described by general relativity makes a "fictitious force" appear in a frame of reference different from a moving, gravitating body. Gravitation is a natural Phenomenon by which objects with Mass attract one another General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent Force that acts on all masses in a non-inertial See also Inertial frame A frame of reference in Physics, may refer to a Coordinate system or set of axes within which to By analogy with electromagnetism, this fictitious force is called the gravitomagnetic force, since it arises in the same way that a moving electric charge creates a magnetic field, the analogous "fictitious force" in special relativity. A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent Force that acts on all masses in a non-inertial Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial The main consequence of the gravitomagnetic force, or acceleration, is that a free-falling object near a massive rotating object will itself rotate. This prediction, often loosely referred to as a gravitomagnetic effect, is among the last basic predictions of general relativity yet to be directly tested.

Indirect validations of gravitomagnetic effects have been derived from analyses of relativistic jets. The lower-energy non-relativistic version of this phenomenon is described at Polar jet. Sir Roger Penrose had proposed a frame dragging mechanism for extracting energy and momentum from rotating black holes. Sir Roger Penrose, PhD, OM, FRS (born 8 August 1931) is an English Mathematical physicist and Emeritus A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e ^[1] Reva Kay Williams, University of Florida, developed a rigorous proof that validated Penrose's mechanism. ^[2] Her model showed the Lense-Thirring effect could account for the observed high energies and luminosities of quasars and active galactic nuclei; the collimated jets about their polar axis; and the asymmetrical jets (relative to the orbital plane). Albert Einstein 's theory of General relativity predicts that rotating bodies drag Spacetime around themselves in a phenomenon referred to as frame-dragging A quasar (contraction of QUASi-stellAR radio source) is an extremely powerful and distant Active galactic nucleus. An active galactic nucleus ( AGN) is a compact region at the centre of a Galaxy which has a much higher than normal luminosity over some or all of the Electromagnetic ^[3] All of those observed properties could be explained in terms of gravitomagnetic effects. ^[4] Williams’ application of Penrose’s mechanism can be applied to black holes of any size. ^[5] Subsequently, relativistic jets can serve as the largest and brightest form of validations for gravitomagnetism.

A group at Stanford University is currently analyzing data from the first direct test of GEM, the Gravity Probe B satellite experiment. Leland Stanford Junior University, commonly known as Stanford University or simply Stanford, is a private Research university located in Gravity Probe B ( GP-B) is a Satellite -based mission which launched in 2004

Equations

According to general relativity, the gravitational field produced by a rotating object (or any rotating mass-energy) can, in a particular limiting case, be described by equations that have the same form as the magnetic field in classical electromagnetism. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 A gravitational field is a model used within Physics to explain how gravity exists in the universe In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Classical electromagnetism (or classical electrodynamics) is a theory of Electromagnetism that was developed over the course of the 19th century most prominently Starting from the basic equation of general relativity, the Einstein field equation, and assuming a weak gravitational field or reasonably flat spacetime, Lano, ^[6] Agop, Buzea and Ciobanu, ^[7] Mashhoon, Gronwald, and Lichtenegger,^[8] and Clark and Tucker,^[9] have derived the following gravitational analogs to Maxwell's equations for electromagnetism, called the "GEM equations":

$\nabla \cdot \mathbf{E} = -4 \pi G \rho \$

$\nabla \cdot \mathbf{B} = 0 \$

$\nabla \times \mathbf{E} = -\frac{1}{c} \frac{\partial \mathbf{B} } {\partial t} \$

$\nabla \times \mathbf{B} = \frac{1}{c} \left( -4 \pi G \mathbf{J} + \frac{\partial \mathbf{E}} {\partial t} \right) = \frac{1}{c} \left( -4 \pi G \rho \mathbf{v}_{\rho} + \frac{\partial \mathbf{E}} {\partial t} \right) \$

where:

E is the static gravitational field (conventional gravity, also called gravitoelectric for the sake of analogy);
B is the gravitomagnetic field;
ρ is mass density (instead of electric charge density);
v_ρ is the velocity of the mass flow generating the gravitomagnetic field;
J is mass current density (J = ρ v_ρ);
G is the gravitational constant;
c is the speed of propagation of gravity (equal to, by general relativity, the speed of light). 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 A gravitational field is a model used within Physics to explain how gravity exists in the universe In Physics and Mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einstein's theory of Special relativity In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of A gravitational field is a model used within Physics to explain how gravity exists in the universe Gravitation is a natural Phenomenon by which objects with Mass attract one another The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different The linear surface or volume charge density is the amount of Electric charge in a line, Surface, or Volume. In Physics, velocity is defined as the rate of change of Position. Current density is a measure of the Density of flow of a conserved charge. The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass In the context of Classical theories of gravitation, the speed of gravity refers to the Speed at which a Gravitational field propagates General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916

For a test particle whose mass m is "small," the net (Lorentz) force acting on it due to a GEM field is described by the following GEM analog to the Lorentz force equation:

$\mathbf{F}_{m} = m \left( \mathbf{E} + \frac{\mathbf{v}_{m}} {c} \times 2 \mathbf{B} \right)$ . In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation

where:

m is the mass of the test particle;
v_m is the instantaneous velocity of the test particle. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object In physical theories, a test particle is an idealized model of an object whose physical properties (usually Mass, Charge, or size) are assumed In Physics, velocity is defined as the rate of change of Position.

In the literature, all instances of B in the GEM equations are multiplied by 1/2, a factor absent from Maxwell's equations. This factor vanishes if B in the GEM version of the Lorentz force equation is multiplied by 2, as shown above. In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation The factors 2 and 1/2 arise because the effective gravitomagnetic charge is twice the static gravitational (gravitoelectric) charge, a remnant of the spin-2 character of the gravitational field. A gravitational field is a model used within Physics to explain how gravity exists in the universe For a pure spin-1 field such as the genuine electromagnetic field, the magnetic charge equals the electric charge. The electromagnetic field is a physical field produced by electrically charged objects. In Physics, a magnetic monopole is a hypothetical particle that is a Magnet with only one pole (see Maxwell's equations for more on magnetic Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction.

For the field B near a rotating body from GEM equations follows:

$\mathbf{B} = \frac{G }{2 c^2} \frac{\mathbf{L} - 3(\mathbf{L} \cdot \mathbf{r}/r) \mathbf{r}/r}{r^3},$

where L is the angular momentum of the body.

Comparison with electromagnetism

The above GEM equations are very similar to Maxwell's equations in free space, which in cgs units are:

$\nabla \cdot \mathbf{E} = 4\pi\rho$

$\nabla \cdot \mathbf{B} = 0$

$\nabla \times \mathbf{E} = -\frac{1}{c} \frac{\partial \mathbf{B}} {\partial t}$

$\nabla \times \mathbf{B} = \frac{1}{c} \left( \frac{\partial \mathbf{E}} {\partial t} + 4\pi \mathbf{J} \right)$

Adopting Planck units eliminates G and c from both sets of equations by normalizing these constants to 1. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric The centimetre-gram-second system ( CGS) is a system of physical units. Planck units are Units of measurement named after the German physicist Max Planck, who first proposed them in 1899 The two sets of equations are now identical but for the minus sign preceding 4π in the GEM equations. These two minus signs stem from an essential difference between gravity and electromagnetism: electrostatic charges of identical sign repel each other, while two like signed (positive) masses attract each other. Gravitation is a natural Phenomenon by which objects with Mass attract one another Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of Electrostatics is the branch of Science that deals with the Phenomena arising from what seems to be stationary Electric charges Since Classical Hence the GEM equations are simply Maxwell's equations with mass (or mass density) substituting for charge (or charge density), and -G replacing the Coulomb force constant 1/(4πε₀). In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different In Physics, a charge may refer to one of many different quantities such as the Electric charge in Electromagnetism or the Color charge in The linear surface or volume charge density is the amount of Electric charge in a line, Surface, or Volume. Vacuum permittivity, referred to by international standards organizations as the electric constant, and denoted by the symbol ε0 is a fundamental Physical The following Table summarizes the results thus far:

Common Structure of the Maxwell and GEM Equations Given Planck units. Planck units are Units of measurement named after the German physicist Max Planck, who first proposed them in 1899
$\nabla \cdot \mathbf{E} = \iota 4\pi\rho$ $\nabla \cdot \mathbf{B} = 0$ $\nabla \times \mathbf{E} = -\partial \mathbf{B}/ \partial t$ $\nabla \times \mathbf{B} = \iota 4\pi\mathbf{J} + \partial \mathbf{E}/ \partial t$ ι = 1 (Maxwell) or -1 (GEM).

The factor of 4π remains in both the GEM and Maxwell's equations because G and 1/(4πε₀) are normalized to 1, and not 4πG and ε₀.

Higher-order effects

Some higher-order gravitomagnetic effects can reproduce effects reminiscent of the interactions of more conventional polarized charges. For instance, if two wheels are spun on a common axis, the mutual gravitational attraction between the two wheels arguably ought to be greater if they spin in opposite directions than in the same direction. This can be expressed as an attractive or repulsive gravitomagnetic component.

Gravitomagnetic arguments also predict that a flexible or fluid toroidal mass undergoing minor axis rotation ("smoke ring" rotation) will tend to pull matter preferentially in through one throat and expel it from the other (a case of rotational frame dragging, acting through the throat). In Geometry, the semi-minor axis (also semiminor axis) is a Line segment associated with most Conic sections (that is with ellipses and In theory, this configuration might be used for accelerating objects (through the throat) without such objects experiencing any g-forces. g-force (also G-force, g-load) is a measurement of an object's Acceleration expressed in g s ^[10]

Consider a toroidal mass with two degrees of rotation (both major axis and minor-axis spin, both turning inside out and revolving). This represents a "special case" in which gravitomagnetic effects generate a chiral corkscrew-like gravitational field around the object. A phenomenon is said to be chiral if it is not identical to its Mirror image (see Chirality) The reaction forces to dragging at the inner and outer equators would normally be expected to be equal and opposite in magnitude and direction respectively in the simpler case involving only minor-axis spin. When both rotations are applied simultaneously, these two sets of reaction forces can be said to occur at different depths in a radial Coriolis field that extends across the rotating torus, making it more difficult to establish that cancellation is complete. In Theoretical physics a Coriolis field is the apparent gravitational field felt by a Rotating or forcibly- accelerated body

Modelling this complex behaviour as a curved spacetime problem has yet to be done and is believed very difficult.

Gravitomagnetic field of Earth

Bg, Earth = 10⁻¹⁴ rad·s⁻¹^[11]

See the Gravity Probe B experiment. Gravity Probe B ( GP-B) is a Satellite -based mission which launched in 2004

Fringe physics

Incomplete understanding of the meaning of the similarity of the gravitomagnetic formulas, above, and Maxwell's equations for (real) electricity and magnetism have given rise to fringe physics. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of Fringe science is scientific Inquiry in an established Field of study which departs significantly from Mainstream or Orthodox Use of the gravitomagnetic analogy for a simplified form of the Einstein field equations, on the other hand, is firmly part 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 General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 It is an approximation to the current standard theory of gravitation, and has testable predictions, which are in the final stages of being directly tested by the Gravity Probe B experiment. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 Gravity Probe B ( GP-B) is a Satellite -based mission which launched in 2004 Despite the use of the word magnetism in gravitomagnetism, and despite the similarity of the GEM force laws to the (real) electromagnetic force law, gravitomagnetism should not be confused with any of the following:

Claims to have constructed anti-gravity devices;
Eugene Podkletnov's claims to have constructed gravity-shielding devices and gravitational reflection beams. In Physics, the electromagnetic force is the force that the Electromagnetic field exerts on electrically charged particles Anti-gravity is the idea of creating a place or object that is free from the force of Gravity. Dr Yevgeny Podkletnov (Евгений Подклетнов is a Russian engineer formerly affiliated with the Materials Science Department at the Tampere University
Any proposal to produce gravitation using electrical circuits.

References

Citations and notes

^ Penrose, R. (1969). Gravitational collapse: The role of general relativity. Nuovo Cimento Rivista, Numero Speciale 1, 252-276.
^ Williams, R. K. (1995, May 15). Extracting x rays, Ύ rays, and relativistic e^-e⁺ pairs from supermassive Kerr black holes using the Penrose mechanism. Physical Review, 51(10), 5387-5427.
^ Williams, R. K. (2004, August 20). Collimated escaping vortical polar e^-e⁺ jets intrinsically produced by rotating black holes and Penrose processes. The Astrophysical Journal, 611, 952-963.
^ Williams, R. K. (2005). Gravitomagnetic field and Penrose scattering processes. Annals of the New York Academy of Sciences, 1045, 232-245.
^ Williams, R. K. (2001, October 15). Collimated energy-momentum extraction from rotating black holes in quasars and microquasars using the Penrose mechanism. AIP Conference Proceedings, 586, 448-453. (http://arxiv.org/abs/astro-ph/0111161)
^ R. P. Lano (1996-03-12). "Gravitational Meissner Effect". arXiv: hep-th 9603077.
^ M. Agop, C. Gh. Buzea and B. Ciobanu (1999-11-10). "On Gravitational Shielding in Electromagnetic Fields.". arXiv: physics 9911011.
^ Mashhoon, Gronwald, Lichtenegger (1999-12-08). "Gravitomagnetism and the Clock Effect". arXiv:General Relativity and Quantum Cosmology 9912027.
^ http://www.iop.org/EJ/article/0264-9381/17/19/311/q01911.pdf
^ Forward, R. L. 1963. Guidelines to Antigravity. American Journal of Physics. 31: 166-170
^ "Experimental Detection of the Gravitomagnetic London Moment" by Martin Tajmar, Florin Plesescu, Klaus Marhold & Clovis J. de Matos

General information

Clark, S J; R W Tucker (2000). "Gauge symmetry and gravito-electromagnetism" (subscription required). Class. Quantum Grav. 17: 4125–4157. doi:10.1088/0264-9381/17/19/311. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.
Forward, Robert (1963) "Guidelines to antigravity," American Journal of Physics 31: 166-70 (Members only access).
Jantzen, Robert T. ; Carini, Paolo; and Bini, Donato (1992). "The Many Faces of Gravitoelectromagnetism". Ann. Physics 215: 1–50. doi:10.1016/0003-4916(92)90297-Y. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document. eprint version
Mashhoon, Bahram (2000). "Gravitoelectromagnetism" arxiv:gr-qc/0011014.
Mashhoon, Bahram (2003). "Gravitoelectromagnetism: a Brief Review" arxiv:gr-qc/0311030. In: Iorio, L. (Ed. ), Measuring Gravitomagnetism: A Challenging Enterprise, Nova Publishers, Hauppauge (NY), pp. 29-39, 2007. A recent introduction to GEM by a leading expert.
Tajmar, M. ; and de Matos, C. J. (2001). "Gravitomagnetic Barnett Effect". Indian J. Phys. B 75: 459–461.
John Archibald Wheeler (1990) A journey into gravity and spacetime. John Archibald Wheeler ( July 9, 1911 &ndash April 13, 2008) was an eminent American Theoretical physicist. See pp. 232-233 ("Gravity's next prize: Gravitomagnetism").
Lorenzo Iorio, (Ed. ) Measuring Gravitomagnetism: A Challenging Enterprise, Nova Publishers, Hauppauge (NY), 2007. ISBN 1-60021-002-3
Jefimenko, Oleg D., "Causality, electromagnetic induction, and gravitation : a different approach to the theory of electromagnetic and gravitational fields". Oleg D Jefimenko is a Physicist and Professor Emeritus at West Virginia University. Star City [West Virginia] : Electret Scientific Co. , c1992. ISBN 0917406095
Heaviside, Oliver, "A gravitational and electromagnetic analogy". The Electrician, 1893.

External links

Gyroscopic Superconducting Gravitomagnetic Effectsnews on tentative result of European Space Agency (esa) research
In Search of gravitomagnetism, NASA, 20 April 2004. Anti-gravity is the idea of creating a place or object that is free from the force of Gravity. The geodetic effect represents the effect of the curvature of Spacetime, predicted by General relativity, on a spinning moving body In Physics, a gravitational wave is a Fluctuation in the Curvature of Spacetime which propagates as a wave, traveling outward from Gravity Probe B ( GP-B) is a Satellite -based mission which launched in 2004 Albert Einstein 's theory of General relativity predicts that rotating bodies drag Spacetime around themselves in a phenomenon referred to as frame-dragging The European Space Agency ( ESA) established in 1975 is an intergovernmental organisation dedicated to the exploration of space, currently with 17 member
Gravitomagnetic London Moment-New test of General Relativity?
Measurement of Gravitomagnetic and Acceleration Fields Around Rotating Superconductors M. Tajmar, et al. , 17 October 2006.
Test of the Lense-Thirring effect with the MGS Mars probe, New Scientist, January 2007.

Dictionary

-noun

(physics) The property of a spinning mass that twists spacetime

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