Gravito-electromagnetic analogies

Costa, L. Filipe O.; Natário, José

doi:10.1007/s10714-014-1792-1

Cited by 58 publications

(106 citation statements)

References 96 publications

(242 reference statements)

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“…By "inertial GEM fields", we mean the fields of inertial forces that arise from the 1+3 splitting of spacetime: the gravitoelectric field G, which plays in this framework a role analogous to the electric field of electromagnetism, and the gravitomagnetic field H, analogous to the magnetic field. We discuss these fields in detail in [14].…”

Section: Tensors Resulting From a Measurement Processmentioning

confidence: 99%

“…The analogy was later cast in exact forms in e.g. [4,6,12,13]; these are not covariant, holding only in specific frames, but (in the more general formulations in [12][13][14] and herein) the test particle can be moving with arbitrary velocity in an arbitrary field.…”

mentioning

confidence: 99%

“…[15][16][17]), this one a purely formal one (see [14]), relating the quadratic scalar invariants of the Maxwell and Weyl tensors [15,16,18], which proves useful in some applications.…”

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confidence: 99%

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Spacetime dynamics of spinning particles: Exact electromagnetic analogies

2016

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We compare the rigorous equations describing the motion of spinning test particles in gravitational and electromagnetic fields, and show that if the Mathisson-Pirani spin condition holds then exact gravito-electromagnetic analogies emerge. These analogies provide a familiar formalism to treat gravitational problems, as well as a means for comparing the two interactions. Fundamental differences are manifest in the symmetries and time projections of the electromagnetic and gravitational tidal tensors. The physical consequences of the symmetries of the tidal tensors are explored comparing the following analogous setups: magnetic dipoles in the field of non-spinning/spinning charges, and gyroscopes in the Schwarzschild, Kerr, and Kerr-de Sitter spacetimes. The implications of the time projections of the tidal tensors are illustrated by the work done on the particle in various frames; in particular, a reciprocity is found to exist: in a frame comoving with the particle, the electromagnetic (but not the gravitational) field does work on it, causing a variation of its proper mass; conversely, for "static observers", a stationary gravitomagnetic (but not a magnetic) field does work on the particle, and the associated potential energy is seen to embody the Hawking-Wald spin-spin interaction energy. The issue of hidden momentum, and its counterintuitive dynamical implications, is also analyzed. Finally, a number of issues regarding the electromagnetic interaction and the physical meaning of Dixon's equations are clarified.

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Section: Tensors Resulting From a Measurement Processmentioning

confidence: 99%

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confidence: 99%

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Spacetime dynamics of spinning particles: Exact electromagnetic analogies

2016

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“…The electric-type tensor is featured in the geodesic deviation equation [34,37,38] have pointed out the role of the magnetic-type tensor in generating a differential precession ΔΩ a for gyroscopes on neighboring geodesics: ΔΩ a ¼ B ab ζ b .…”

Section: Analysis a Tidal Tensorsmentioning

confidence: 99%

Tidal invariants for compact binaries on quasicircular orbits

et al. 2015

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We extend the gravitational self-force approach to encompass "self-interaction" tidal effects for a compact body of mass μ on a quasicircular orbit around a black hole of mass M ≫ μ. Specifically, we define and calculate at OðμÞ (conservative) shifts in the eigenvalues of the electric-and magnetic-type tidal tensors, and a (dissipative) shift in a scalar product between their eigenbases. This approach yields four gauge-invariant functions, from which one may construct other tidal quantities such as the curvature scalars and the speciality index. First, we analyze the general case of a geodesic in a regular perturbed vacuum spacetime admitting a helical Killing vector and a reflection symmetry. Next, we specialize to focus on circular orbits in the equatorial plane of Kerr spacetime at OðμÞ. We present accurate numerical results for the Schwarzschild case for orbital radii up to the light ring, calculated via independent implementations in Lorenz and Regge-Wheeler gauges. We show that our results are consistent with leading-order postNewtonian expansions, and demonstrate the existence of additional structure in the strong-field regime. We anticipate that our strong-field results will inform (e.g.) effective one-body models for the gravitational two-body problem that are invaluable in the ongoing search for gravitational waves.

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“…[17]). It is an important property of our fluid that we do not need such a supplementary condition as the dynamics of the spin tensor (26) is completely fixed by the EOMs for n, u μ and the field q μ .…”

Section: From the Lagrangian (16) We Derive The Euler-lagrange Eomsmentioning

confidence: 99%

General relativistic, nonstandard model for the dark sector of the Universe

Stichel

Zakrzewski

2015

Eur. Phys. J. C

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We present a general relativistic version of the self-gravitating fluid model for the dark sector of the Universe (darkon fluid) introduced in Stichel and Zakrzewski (Phys Rev D 80:083513, 2009) and extended and reviewed in Stichel and Zakrzewski (Entropy 15:559, 2013). This model contains no free parameters in its Lagrangian. The resulting energy-momentum tensor is dustlike with a nontrivial energy flow. In an approximation valid at sub-Hubble scales we find that the present-day cosmic acceleration is not attributed to any kind of negative pressure but it is due to a dynamically determined negative energy density. This property turns out to be equivalent to a time-dependent spatial curvature. The obtained cosmological equations, at sub-Hubble scales, agree with those of the nonrelativistic model but they are given a new physical interpretation. Furthermore, we have derived the self-consistent equation to be satisfied by the nonrelativistic gravitational potential produced by a galactic halo in our model from a weak-field limit of a generalized TolmanOppenheimer-Volkoff equation.

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Gravito-electromagnetic analogies

Cited by 58 publications

References 96 publications

Spacetime dynamics of spinning particles: Exact electromagnetic analogies

Spacetime dynamics of spinning particles: Exact electromagnetic analogies

Tidal invariants for compact binaries on quasicircular orbits

General relativistic, nonstandard model for the dark sector of the Universe

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