Explicit Fermi coordinates and tidal dynamics in de Sitter and Gödel spacetimes

Chicone, Carmen; Mashhoon, Bahram

doi:10.1103/physrevd.74.064019

Cited by 74 publications

(125 citation statements)

References 37 publications

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“…In previous work on tidal dynamics [3][4][5][6][7][8][9], the relative behavior of a congruence of geodesics has been studied. Moreover, tidal gravitational acceleration of ultrarelativistic particles has been considered in a general context but via geodesic deviation within the small-deviation approximation [4][5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Double-Kasner spacetime: Peculiar velocities and cosmic jets

2011

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In dynamic spacetimes in which asymmetric gravitational collapse/expansion is taking place, the timelike geodesic equation appears to exhibit an interesting property: Relative to the collapsing configuration, free test particles undergo gravitational "acceleration" and form a double-jet configuration parallel to the axis of collapse.We illustrate this aspect of peculiar motion in simple spatially homogeneous cosmological models such as the Kasner spacetime. To estimate the effect of spatial inhomogeneities on cosmic jets, timelike geodesics in the Ricci-flat double-Kasner spacetime are studied in detail. While spatial inhomogeneities can significantly modify the structure of cosmic jets, we find that under favorable conditions the double-jet pattern can initially persist over a finite period of time for sufficiently small inhomogeneities.

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Section: Introductionmentioning

confidence: 99%

Double-Kasner spacetime: Peculiar velocities and cosmic jets

2011

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“…To express this trajectory in terms of the original background coordinate system, it is in general necessary to have the explicit coordinate transformation between the two systems of coordinates. This turns out to be possible only in very special situations [38,39]. However, our first-order approximation scheme makes it possible to proceed as follows.…”

Section: Appendix A: Mpd Equations In Fermi Normal Coordinatesmentioning

confidence: 99%

Dynamics of extended spinning masses in a gravitational field

2006

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We develop a first-order approximation method for the influence of spin on the motion of extended spinning test masses in a gravitational field. This approach is illustrated for approximately circular equatorial motion in the exterior Kerr spacetime. In this case, the analytic results for the first-order approximation are compared to the numerical integration of the exact system and the limitations of the first-order results are pointed out. Furthermore, we employ our analytic results to illustrate the gravitomagnetic clock effect for spinning particles.

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“…Taking the variational derivatives with respect toḡ µν from the expressions (137) and (138), and applying thermodynamic equations (18), allows us to write down the right sides of equations (134b), (134c) as follows,…”

Section: The Gravitational Field Perturbationsmentioning

confidence: 99%

“…Transformation from the preferred cosmological frame to the local chart must include the Lorentz boost and a geometric part due to the expansion and curvature of cosmological spacetime. It can take on multiple forms which originate from certain geometric and/or experimental requirements [16,18,48,54].We do not impose specific limitations on the choice of coordinates on the background manifold and keep the overall formalism of the post-Newtonian approximations, covariant. The arbitrary coordinates are denoted as x α = (x 0 , x i ) and they are related to the preferred isotropic coordinates X α = (η, X i ) by the coordinate transformation x α = x α X β .…”

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Post-Newtonian celestial dynamics in cosmology: Field equations

Kopeikin

Петров

2013

Phys. Rev. D

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Post-Newtonian celestial dynamics is a relativistic theory of motion of massive bodies and test particles under the influence of relatively weak gravitational forces. Standard approach for development of this theory relies upon the key concept of the isolated astronomical system supplemented by the assumption that the background space-time is flat. The standard post-Newtonian theory of motion was instrumental in explanation of the existing experimental data on binary pulsars, satellite and lunar laser ranging, and in building precise ephemerides of planets in the solar system. Recent studies of the formation of large-scale structure in our universe indicate that the standard post-Newtonian mechanics fails to describe more subtle dynamical effects in motion of the bodies comprising the astronomical systems of larger size -galaxies and clusters of galaxies -where the Riemann curvature of the expanding FLRW universe interacts with the local gravitational field of the astronomical system and, as such, can not be ignored.The present paper outlines theoretical principles of the post-Newtonian mechanics in the expanding universe. It is based upon the gauge-invariant theory of the Lagrangian perturbations of cosmological manifold caused by an isolated astronomical N-body system (the solar system, a binary star, a galaxy, a cluster of galaxies). We postulate that the geometric properties of the background manifold are described by a homogeneous and isotropic Friedman-Lemaître-Robertson-Walker (FLRW) metric governed by two primary components -the dark matter and the dark energy. The dark matter is treated as an ideal fluid with the Lagrangian taken in the form of pressure along with the scalar Clebsch potential as a dynamic variable. The dark energy is associated with a single scalar field with a potential which is hold unspecified as long as the theory permits. Both the Lagrangians of the dark matter and the scalar field are formulated in terms of the field variables which play a role of generalized coordinates in the Lagrangian formalism. It allows us to implement the powerful methods of variational calculus to derive the gauge-invariant field equations of the post-Newtonian celestial mechanics of an isolated astronomical system in an expanding universe. These equations generalize the field equations of the post-Newtonian theory in asymptotically-flat spacetime by taking into account the cosmological effects explicitly and in a self-consistent manner without assuming the principle of liner superposition of the fields or a vacuole model of the isolated system, etc. The field equations for matter dynamic variables and gravitational field perturbations are coupled in the most general case of arbitrary equation of state of matter of the background universe.We introduce a new cosmological gauge which generalizes the de Donder (harmonic) gauge of the post-Newtonian theory in asymptotically flat spacetime. This gauge significantly simplifies the gravitational field equations and allows to find out the approximations where the ...

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Explicit Fermi coordinates and tidal dynamics in de Sitter and Gödel spacetimes

Cited by 74 publications

References 37 publications

Double-Kasner spacetime: Peculiar velocities and cosmic jets

Double-Kasner spacetime: Peculiar velocities and cosmic jets

Dynamics of extended spinning masses in a gravitational field

Post-Newtonian celestial dynamics in cosmology: Field equations

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