Tidal dynamics in cosmological spacetimes

Mashhoon, Bahram; Mobed, Nader; Singh, Dinesh

doi:10.1088/0264-9381/24/20/008

Cited by 42 publications

(68 citation statements)

References 38 publications

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“…Bonnor [11] concluded that the local systems expand but at a rate which is negligible compared with the general cosmic expansion. Similar conclusion was reached by Mashhoon et al [77] who analysed the tidal dynamics of test particles in the Fermi coordinates.The vacuole solutions are not appropriate for adequate physical solution of the N-body problem in the expanding universe. There are several reasons for it.…”

supporting

confidence: 83%

“…Current paradigm is that the cosmological generalization of the Newtonian field equations of an isolated gravitating system like the solar system or a galaxy or a cluster of galaxies can be easily obtained by just making use of the linear principle of superposition with a simple algebraic addition of the local system to the tensor of energy momentum of the background matter. It is assumed that the superposition procedure is equivalent to operating with the Newtonian equations of motion derived in asymptotically-flat spacetime and adding to them ("by hands") the tidal force due to the presence of the external universe (see, for example, [77]). Though such a procedure may look pretty obvious it lacks a rigorous mathematical analysis of the perturbations induced on the background cosmological manifold by the local system.…”

Section: Brief History Of Cosmological Perturbation Theorymentioning

confidence: 99%

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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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supporting

confidence: 83%

Section: Brief History Of Cosmological Perturbation Theorymentioning

confidence: 99%

Post-Newtonian celestial dynamics in cosmology: Field equations

Kopeikin

Петров

2013

Phys. Rev. D

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“…As in the case of the PA and, to a lesser extent so far, the FA, also such an alleged anomaly motivated many researches to find viable explanations in terms of various either conventional or unconventional physical mechanisms. 159,206,[282][283][284][285][286][287][288][289][290][291][292][293][294][295][296] The various attempts 154,[279][280][281] to investigate it have been performed so far within the framework of the International Astronomical Union (IAU) 1976 System of Astronomical Constants, available on the Internet at http://www.iau.org/static/resolutions/ IAU1976_French.pdf, which, in turn, is reminiscent of pre-relativistic eras when, among other things, only relative distances (expressed in astronomical units) in the Solar system could be determined since absolute ones could not be estimated with high accuracy. More precisely, the IAU 1976 system prescribed to measure the masses in units of Solar masses, the durations in days D (made of 86400 seconds), and the distances in astronomical units of length.…”

Section: The Anomalous Secular Increase Of the Astronomical Unitmentioning

confidence: 99%

Gravitational anomalies in the solar system?

Iorio

2015

Int. J. Mod. Phys. D

100

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Mindful of the anomalous perihelion precession of Mercury discovered by U. Le Verrier in the second half of the nineteenth century and its successful explanation by A. Einstein with his General Theory of Relativity in the early years of the twentieth century, discrepancies among observed effects in our Solar system and their theoretical predictions on the basis of the currently accepted laws of gravitation applied to known matter-energy distributions have the potential of paving the way for remarkable advances in fundamental physics. This is particularly important now more than ever, given that most of the universe seems to be made of unknown substances dubbed Dark Matter and Dark Energy. Should this not be directly the case, Solar system's anomalies could anyhow lead to advancements in either cumulative science, as shown to us by the discovery of Neptune in the first half of the nineteenth century, and technology itself. Moreover, investigations in one of such directions can serendipitously enrich the other one as well. The current status of some alleged gravitational anomalies in the Solar system is critically reviewed. They are: a) Possible anomalous advances of planetary perihelia; b) Unexplained orbital residuals of a recently discovered moon of Uranus (Mab); c) The lingering unexplained secular increase of the eccentricity of the orbit of the Moon; d) The so-called Faint Young Sun Paradox; e) The secular decrease of the mass parameter of the Sun; f) The Flyby Anomaly; g) The Pioneer Anomaly; and h) The anomalous secular increase of the astronomical unit

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“…The metric (20) describes a spherically symmetric and dynamical black hole in a FRW background more general than de Sitter. In this case, the event horizon may not be well-defined, but the AH always exists.…”

Section: Evolution Of the Apparent Horizonsmentioning

confidence: 99%

Black holes in the Universe: Generalized Lemaître-Tolman-Bondi solutions

et al. 2011

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We present new exact solutions which presumably describe black holes in the background of a spatially flat, pressureless dark matter (DM)-, or dark matter plus dark energy (DM+DE)-, or quintom-dominated universe. These solutions generalize Lemaître-Tolman-Bondi metrics. For a DM-or (DM+DE)-dominated universe, the area of the black hole apparent horizon (AH) decreases with the expansion of the universe while that of the cosmic AH increases. However, for a quintomdominated universe, the black hole AH first shrinks and then expands, while the cosmic AH first expands and then shrinks. A (DM+DE)-dominated universe containing a black hole will evolve to the Schwarzschild-de Sitter solution with both AHs approaching constant size. In a quintomdominated universe, the black hole and cosmic AHs will coincide at a certain time, after which the singularity becomes naked, violating Cosmic Censorship.

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Tidal dynamics in cosmological spacetimes

Cited by 42 publications

References 38 publications

Post-Newtonian celestial dynamics in cosmology: Field equations

Post-Newtonian celestial dynamics in cosmology: Field equations

Gravitational anomalies in the solar system?

Black holes in the Universe: Generalized Lemaître-Tolman-Bondi solutions

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