Fermi normal co-ordinate system and electromagnetic detectors of gravitational waves

Fortini, P.; Gualdi, C.

doi:10.1007/bf02721692

Cited by 44 publications

(45 citation statements)

References 3 publications

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“…The third-and fourth-order approximations for Fermi normal coordinates in arbitrary spacetime were derived by Li and Ni [21,22]. The next important result was obtained by Fortini and Gualdi [12] who succeeded in deriving the series expansion to all orders in the distance parameters for spacetime in which a plane gravitational wave is propagating in a flat background. The formulae of Fortini and Gualdi were later generalized by Marzlin [23] for an arbitrary weak-field geometry of spacetime and accelerating observers.…”

Section: Overview Of Riemann and Fermi Normal Coordinatesmentioning

confidence: 99%

Fermi-normal, optical, and wave-synchronous coordinates for spacetime with a plane gravitational wave

Rakhmanov

2014

Class. Quantum Grav.

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Abstract. Fermi normal coordinates provide a standardized way to describe the effects of gravitation from the point of view of an inertial observer. These coordinates have always been introduced via perturbation expansions and were usually limited to distances much less than the characteristic length scale set by the curvature of spacetime. For a plane gravitational wave this scale is given by its wavelength which defines the domain of validity for these coordinates known as the long-wavelength regime. The symmetry of this spacetime, however, allows us to extend Fermi normal coordinates far beyond the long-wavelength regime. Here we present an explicit construction for this long-range Fermi normal coordinate system based on the unique solution of the boundary-value problem for spacelike geodesics. The resulting formulae amount to summation of the infinite series for Fermi normal coordinates previously obtained with perturbation expansions. We also consider two closely related normal coordinate systems: optical coordinates which are built from null geodesics and wave-synchronous coordinates which are built from spacelike geodesics locked in phase with the propagating gravitational wave. The wave-synchronous coordinates yield the exact solution of Peres and Ehlers-Kundt which is globally defined. In this case, the limitation of the longwavelength regime is completely overcome, and the system of wave-synchronous coordinates becomes valid for arbitrarily large distances. Comparison of the different coordinate systems is done by considering the motion of an inertial test mass in the field of a plane gravitational wave.

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Section: Overview Of Riemann and Fermi Normal Coordinatesmentioning

confidence: 99%

Fermi-normal, optical, and wave-synchronous coordinates for spacetime with a plane gravitational wave

Rakhmanov

2014

Class. Quantum Grav.

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“…For a nonrotating frame (i.e. when the vectors h (n) i are displaced along the basis line (2) according to the Fermi-Walker transport) the quantities {X (α) , cτ} correspond to the Fermi normal coordinates (see for instance [14,15,16]). Analogous quantities…”

Section: Comoving Reference Framementioning

confidence: 99%

The Equations of Motion of Compact Binaries in the Neighborhood of Supermassive Black Hole

Gorbatsievich

Bobrik

Ruffini³

et al. 2010

AIP Conference Proceedings

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Abstract. By the use of Einstein-Infeld-Hoffmann method, the equations of motion of a binary star system in the field of a supermassive black hole are derived. In spite of the fact that the motion of a binary system as a whole can be relativistic or even ultra-relativistic with respect to the supermassive black hole, it is shown, that under the assumption of non-relativistic relative motion of the stars in binary system, the motion of the binary system as a whole satisfies the Mathisson-Papapetrou equations with additional terms depending on quadrupole moments. Exemplary case of ultrarelativistic motion of a binary neutron star in the vicinity of non-rotating black hole is considered. It it shown that the motion of binary's center of mass may considerably differ from geodesic motion.

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“…In fact, the proper reference frame where an observer may execute a measurement is the FNC [14,16]. Therefore any tensor expressed in WRF must be written in FNC.…”

Section: Fnc For An Exact Linearly Polarized Wavementioning

confidence: 99%

“…Therefore any tensor expressed in WRF must be written in FNC. To this aim, this section is devoted to linking the WRF to the laboratory reference frame (FNC); this is accomplished by following the procedure outlined in [14,16]. First, we consider an observer moving along a time-like geodesic in WRF; let q(τ ) be its world line, τ its proper time, and f (0) its four-velocity.…”

Section: Fnc For An Exact Linearly Polarized Wavementioning

confidence: 99%

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Exact Plane Gravitational Waves and Electromagnetic Fields

Montanari

Calura

2000

Annals of Physics

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The behaviour of a "test" electromagnetic field in the background of an exact gravitational plane wave is investigated in the framework of Einstein's general relativity. We have expressed the general solution to the de Rham equations as a Fourier-like integral. In the general case we have reduced the problem to a set of ordinary differential equations and have explicitly written the solution in the case of linear polarization of the gravitational wave. We have expressed our results by means of Fermi Normal Coordinates (FNC), which define the proper reference frame of the laboratory. Moreover we have provided some gedanken experiments, showing that an external gravitational wave induces measurable effects of non tidal nature via electromagnetic interaction. Consequently it is not possible to eliminate gravitational effects on electromagnetic field, even in an arbitrarily small spatial region around an observer freely falling in the field of a gravitational wave. This is opposite to the case of mechanical interaction involving measurements of geodesic deviation effects. This behaviour is not in contrast with the principle of equivalence, which applies to arbitrarily small region of both space and time.

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Fermi normal co-ordinate system and electromagnetic detectors of gravitational waves

Cited by 44 publications

References 3 publications

Fermi-normal, optical, and wave-synchronous coordinates for spacetime with a plane gravitational wave

Fermi-normal, optical, and wave-synchronous coordinates for spacetime with a plane gravitational wave

The Equations of Motion of Compact Binaries in the Neighborhood of Supermassive Black Hole

Exact Plane Gravitational Waves and Electromagnetic Fields

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