Gravitoelectromagnetism (sometimes Gravitomagnetism, Gravimagnetism,
abbreviated GEM), refers to a set of formal analogies between Maxwell's
field equations and an approximation, valid under certain conditions, to the
Einstein field equations for general relativity. The most common version of GEM
is valid only far from isolated sources, and for slowly moving test particles.
Gravitomagnetic forces and the
corresponding field (gravitomagnetic field and gravitational
torsion field in
alternatives to general relativity) should be considered in all reference
frames that move relative to a source of the static gravitational field.
Similarly, the relative motion of an observer with respect to an electrical
charge creates a magnetic field and therefore magnetic force is possible.
Currently, verification of
gravitoelectromagnetic forces are doing with the help of satellites, ^{[1]} and in some experiments. ^{[2]}^{ }^{[3]}
Indirect validations of
gravitomagnetic effects have been derived from analyses of relativistic jets.
Roger Penrose had proposed a frame dragging mechanism for extracting energy and
momentum from rotating black holes.^{[4]} This model
was used to explain the high energies and luminosities in quasars and active
galactic nuclei; the collimated jets about their polar axis; and the
asymmetrical jets (relative to the orbital plane).^{[5]}
^{[6]} All of those observed properties could be
explained in terms of gravitomagnetic effects.^{[7]}
Application of Penrose's mechanism can be applied to black holes of any size.^{[8]} Relativistic jets can serve as the largest and
brightest form of validations for gravitomagnetism.
According to general relativity,
the weak gravitational field produced by a moving or rotating object (or any
moving or rotating massenergy) can, in a particular limiting case, be
described by equations that have the same form as the equations in classical
electromagnetism. Starting from the basic equation of general relativity, the
Einstein field equation, and assuming a weak gravitational field or reasonably
flat spacetime, the gravitational analogs to Maxwell's equations for
electromagnetism, called the "GEM equations", were derived by Lano. ^{[9]}
Subsequently, Agop, Buzea and
Ciobanu, ^{[10]} and others have confirmed the
validity of GEM equations in International System of Units in the following
form:
where:
For a test particle whose mass m
is "small," in a stationary system, the net (Lorentz) force acting on
it due to a GEM field is described by the following GEM analog to the Lorentz
force equation:
where:
Acceleration of any test particle
is simply:
The second component of the
gravitational force responsible for the collimation of relativistic jets in the
gravitomagnetic fields of galaxies, active galactic nuclei and rapidly rotating
stars (e.g., jet accreting neutron stars).
In general relativity, due to the
alleged tensor nature of gravitation considered that the effective mass for the
gravitomagnetic field is twice the usual body mass. Because of this, it is
assumed that either , ^{[11]} or in
some papers . ^{[12]} ^{[13]}
The above equations of the
gravitational field (equation GEM) can be compared with Maxwell's equations:
where:
It can be seen that the form of
the gravitational and electromagnetic fields equations is almost the same,
except for some factors and minus signs in GEM equations arising from the fact
that the masses are attracted, and the electric charges of the same sign repel
each other.
Lorentz force, acting on a
charge , is given by:
Sergey Fedosin with the help of Lorentzinvariant theory of gravitation
(LITG), derived gravitational equation in special relativity. ^{[14]}
where:
The equations coincide with
equations which were first published in 1893 by Oliver Heaviside as a separate
theory expanding Newton's law. ^{[15]}
These equations, called the
Heaviside equations, are Lorentz covariant, unlike equations of
gravitoelektromagnetism. The similarity of Heaviside gravitational equations
and Maxwell's equations for electromagnetic field highlighted in Maxwelllike gravitational equations.
The gravitational force in LITG
is as follows:
In contrast to general
relativity, where spin of gravitons is equal to 2, Lorentzinvariant theory of
gravitation (LITG) relies on vectorial gravitons with spin equal to 1.
Accordingly, in LITG body mass for gravitational and torsion fields is the
same.
Some higherorder effects can
reproduce effects reminiscent of the interactions of more conventional
polarized charges. In torsion field appears momentum of force acting on a rotating particle with the spin :
This leads to precession of the
particle spin with angular velocity around direction of .
The mechanical energy of the
particle with spin in torsion field will be:
If two disks are spun on a common
axis, the mutual gravitational attraction between the two disks 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 force component. When disks
rotate in opposite directions, the energy will be negative, and additional
force of gravitation is equal to
where torsion field of one disk acts on the angular momentum of another disk.
Due to the torsion field becomes
possible effect of gravitational induction.
The formula for torsion field near a rotating body can be derived from the
Heaviside equations and is: ^{[14]}
where is angular momentum of the body, is radiusvector from the center of the body to the point, where the
torsion field defined.
A detailed derivation of this
formula is contained in the book. ^{[16]}
At the equatorial plane, r
and L
are perpendicular, so their dot product vanishes, and this formula reduces
to:
Magnitude of angular momentum of
a homogeneous ballshaped body is:
where:
Therefore, magnitude of Earth's
torsion field at its equator is:
where is the gravity of Earth. The torsion field
direction coincides with the angular moment direction, i.e. north.
As the Earth is only
approximately a homogeneous ball, from this calculation it follows that Earth's
equatorial torsion field is about s^{−1} for the observer, fixed relative to the
stars. Here were used the following data: the angular momentum of the Earth J • s, radius of the Earth m, the speed of gravity is assumed equal to the speed of light. Such a
field is extremely weak and requires extremely sensitive measurements to be
detected. One experiment to measure such field was the Gravity Probe B mission.
If we use the preceding formula
for the second fastestspinning pulsar known, PSR J17482446ad (which rotates
716 times per second), assuming its radius of km, and its mass as two solar masses, then we have
equals about s^{−1}. This is simple estimation
of the field. But the pulsar is spinning at a quarter of the speed of light at
the equator, and its radius is only three times more than its Schwarzschild
radius. When such fast motion and such strong gravitational field exist in a
system, the simplified approach of separating gravitomagnetic and
gravitoelectric forces can be applied only as a very rough approximation.
It is clear those charged and
massive bodies that interact with each other two similar forces (Lorentz force
for charges and gravitoelectromagnetic force for masses), and create around
themselves in the space similar in shape and dependence on the movement
electromagnetic and gravitational fields, may have even something more common.
In particular, we can not exclude the fact that one field, one way or another
does not affect the other field or strength of its interaction. There are some
attempts to describe the connection of both fields, based on the similarity of
the field equations. For example, Fedosin combines both fields into a single
electrogravitational field. ^{[14]} Naumenko
offered his version of combination of the fields. ^{[17]}
Alekseeva builds the model of electrogravitomagnetic field with the help of
biquaternions. ^{[18]} The interaction of gravitation
and electromagnetism is described in some papers of Evans. ^{[19]}
There are published articles that
described a weak shielding of gravity of a test body: 1) With a superconducting
disk, suspended with the help of Meissner effect. ^{[20]}
The rotation of the disc increases the effect. 2) Using a disk of toroidal
form. ^{[21]} The impact of rotation of
superconducting disk on accelerometer is found in some experiments. ^{[22]}
Connection between the field of strong gravitation and the electromagnetic
field of proton is given by the ratio of mass to charge of the particle. On the
base of similarity of matter levels
one can make the transformation of physical quantities and move from a proton
to neutron star (magnetar as analogue of proton), with the replacement of
strong gravitation by normal gravitation. It is assumed that magnetars not only
have a strong magnetic field, but also a positive electric charge.
Consideration of joint evolution of the neutron star and its constituent
nucleons leads to the following conclusion: the maximum charge of object
(neutron star or a proton) is restricted by condition of matter integrity under
action of photons of electromagnetic radiation, associated with the charge of
the object. ^{[23]} Then from the condition of equality of density of vacuum electromagnetic energy
and the energy density of gravitation (derived from Le Sage's theory of
gravitation), the assumption is that gravitons are particles like photons. In
this case, since electrons are actively interacting with photons, we should
expect the influence of electric currents in matter on distribution of
gravitons and magnitude of gravitational forces. This approach allows
explaining the above experiments with superconductors.
Another finding is interaction of
strong gravitational field and electromagnetic field in a hydrogen atom,
arising from the law of redistribution of energy flows. On the one hand, the
equality of gravitational and electrical forces acting on atomic electron, can
set the value of strong gravitation
constant. On the other hand, there is a limit relation of equality of
interaction energies of proton in magnetic field and gravitational torsion
(gravitomagnetic) field of electron.
The concept of general field has brought together not only
the electromagnetic and gravitational fields, but also other vector fields,
including acceleration field, the pressure field, the dissipation field, the fields of strong and
weak interactions in matter. ^{[24]} ^{[25]}
1.
Everitt,
C.W.F., et al., Gravity Probe B: Countdown to Launch. In: Laemmerzahl, C.,
Everitt, C.W.F., Hehl, F.W. (Eds.), Gyros, Clocks, Interferometers...: Testing
Relativistic Gravity in Space. – Berlin, Springer, 2001, pp. 52–82.
2.
Fomalont
E.B., Kopeikin S.M. The Measurement of the Light Deflection from Jupiter:
Experimental Results (2003), Astrophys. J., 598, 704. (astroph/0302294)
3.
Graham,
R.D., Hurst, R.B., Thirkettle, R.J., Rowe, C.H., and Butler, B.H.,
"Experiment to Detect FrameDragging in a Lead Superconductor,"
(2007). [1]
4.
Roger Penrose (1969).
"Gravitational collapse: The role of general relativity". Rivista de Nuovo Cimento, Numero Speciale 1: 252–276.
5.
R.K. Williams (1995).
"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.
6.
R.K. Williams (2004).
"Collimated escaping vortical polar e^{−}e^{+} jets
intrinsically produced by rotating black holes and Penrose processes". The Astrophysical Journal 611: 952–963. doi:10.1086/422304.
7.
R.K. Williams (2005).
"Gravitomagnetic field and Penrose scattering processes". Annals of the New York Academy of Sciences 1045: 232–245.
8.
R.K. Williams (2001).
"Collimated energymomentum extraction from rotating black holes in
quasars and microquasars using the Penrose mechanism". AIP Conference Proceedings 586: 448–453 (arXiv: astroph/0111161).
9.
R.P. Lano (1996).
"Gravitational Meissner Effect". arXiv:
hepth/9603077.
10.
M. Agop, C. Gh.
Buzea, B. Ciobanu (1999). "On Gravitational Shielding in Electromagnetic
Fields". arXiv: physics/9911011.
11.
M. L.
Ruggiero, A. Tartaglia. Gravitomagnetic effects. Nuovo Cim. 117B (2002) 743—768
( grqc/0207065 ), формулы
(24) и (26).
12.
Mashhoon, Gronwald,
Lichtenegger (19991208). "Gravitomagnetism
and the Clock Effect". arXiv:
General Relativity and Quantum Cosmology 9912027.
13.
Clark, S J; R W
Tucker (2000). "Gauge
symmetry and gravitoelectromagnetism". Class. Quantum Grav. 17: 41254157.
14.
^{14.0} ^{14.1} ^{14.2} Fedosin, S.G. (1999), written at Perm, pages 544, Fizika
i filosofiia podobiia ot preonov do metagalaktik, ISBN 5813100121.
15.
Heaviside,
Oliver, A gravitational and
electromagnetic analogy. The Electrician, 1893.
16.
Fedosin
S.G. Fizicheskie teorii i beskonechnaia
vlozhennost’ materii. – Perm, 2009, 844 pages, Tabl. 21, Pic. 41, Ref. 289.
ISBN 9785990195110. (in Russian).
17.
Naumenko
Y.V. Unified Theory of Vector Fields (from
Maxwell's electrodynamics to a unified field theory). Armavir, Armavir
polygraph company, 2006. (In Russian)
18.
Alekseeva
L.A. One biquaternionic
model of electrogravimagnetic field. Field analogs of Newton's laws. 11
Mar. 2007. (In Russian).
19.
Myron W.
Evans. Gravitational
Poynting theorem: interaction of gravitation and electromagnetism. Paper
168. Alpha
Institute for Advanced Studies (AIAS).
20.
Eugene
Podkletnov and R. Nieminen. A Possibility of Gravitational Force Shielding by
Bulk YBa2Cu3O7x Superconductor, Physica C, 1992, pp. 441443.
21.
E.
Podkletnov and A.D. Levit. Gravitational shielding properties of composite bulk
Y Ba2Cu3O7x superconductor below 70 K under electromagnetic field, Tampere
University of Technology report MSUchem, January 1995.
22.
M.
Tajmar, et. al. Measurement of
Gravitomagnetic and Acceleration Fields Around Rotating Superconductors. 17
October 2006.
23.
Fedosin
S.G. Comments to the book: Fizicheskie teorii
i beskonechnaia vlozhennost’ materii. – Perm, 2009, 844 pages, Tabl. 21,
Pic. 41, Ref. 289. ISBN
9785990195110. (in Russian).
24.
Fedosin
S.G. The procedure of finding the
stressenergy tensor and vector field equations of any form. Advanced
Studies in Theoretical Physics, Vol. 8, 2014, no. 18, 771  779. http://dx.doi.org/10.12988/astp.2014.47101.
25. Fedosin
S.G. The Concept of the General Force Vector Field. OALib Journal, Vol. 3, P. 115 (2016), e2459. http://dx.doi.org/10.4236/oalib.1102459.

Source: http://sergf.ru/gmen.htm