Effective refractive index tensor for weak-field gravity

Boonserm, Petarpa; Cattoën, Céline; Faber, Tristan; Visser, Matt; Weinfurtner, Silke

doi:10.1088/0264-9381/22/11/001

Cited by 23 publications

(27 citation statements)

References 17 publications

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“…By an analysis of observed rotation curves, under reasonable assumptions (e.g., that galaxies can be modelled as spherically symmetric) it has been found that the dark matter is of the form of an anisotropic fluid [13]. This has been taken up in [14], in which the consequences of anisotropic dark matter stresses are discussed in the weak field gravitational lensing (where it was noted that any attempt to model dark matter in galactic halos with classical fields will lead to anisotropic stresses comparable in magnitude with the energy density).…”

Section: ∂A(rt) ∂Tmentioning

confidence: 98%

Averaging spherically symmetric spacetimes in general relativity

Coley

Pelavas

2006

Phys. Rev. D

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We discuss the averaging problem in general relativity, using the form of the macroscopic gravity equations in the case of spherical symmetry in volume preserving coordinates. In particular, we calculate the form of the correlation tensor under some reasonable assumptions on the form for the inhomogeneous gravitational field and matter distribution. On cosmological scales, the correlation tensor in a Friedmann-Lemaître-Robertson-Walker (FLRW) background is found to be of the form of a spatial curvature. On astrophysical scales the correlation tensor can be interpreted as the sum of a spatial curvature and an anisotropic fluid. We briefly discuss the physical implications of these results.[PACES: 98.80.Jk,04.50.+h] The gravitational field equations on large scales are obtained by averaging the Einstein equations of general relativity (GR). The Universe is not isotropic or spatially homogeneous on local scales. An averaging of inhomogeneous spacetimes on large scales can lead to important effects. For example, on cosmological scales the dynamical behavior can differ from that in the spatially homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) model [1]; in particular, the expansion rate may be significantly affected. Consequently, a solution of the averaging problem is of considerable importance for the correct interpretation of cosmological data. It is also of importance for physical phenomena on astrophysical (galactic) scales.There are a number of theoretical approaches to the averaging problem [2][3][4]. In the approach of Buchert [4] a 3+1 cosmological space-time splitting is employed and only scalar quantities are averaged. The perturbative approach [2] involves averaging the perturbed Einstein equations; however, a perturbation analysis cannot provide any information about an averaged geometry. On the other hand, the macroscopic gravity (MG) approach to the averaging problem in GR [3] gives a prescription for the correlation functions which emerge in an averaging of field equations. The MG approach is a fully covariant, gauge independent and exact method. We shall adopt the MG averaging approach.Averaging of the structure equations for the geometry of GR then leads to the structure equations for the averaged 1 (macroscopic) geometry and the definitions and the properties of the correlation tensor. The averaged Einstein equations can always be written in the form of the Einstein equations for the macroscopic metric tensor when the correlation terms are moved to the right-hand side of the averaged Einstein equations [3].Spherical symmetry is of particular physical interest, and it is especially important to study the averaging problem within the class of spherically symmetric cosmological models. In [5] the microscopic field equations were taken and the averaging procedure was effected to determine the precise form of the correlation tensor in this case. In volume preserving coordinates (VPC), the spherically symmetric line element is given bywhere the functions A and B depend on t and r....

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Section: ∂A(rt) ∂Tmentioning

confidence: 98%

Averaging spherically symmetric spacetimes in general relativity

Coley

Pelavas

2006

Phys. Rev. D

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“…By an analysis of observed rotation curves, under reasonable assumptions (e.g., that galaxies can be modeled as spherically symmetric) it has been found that the dark matter is of the form of an anisotropic fluid [18]. This has been taken up in [19], in which the consequences of anisotropic dark matter stresses are discussed in the weak field gravitational lensing (where it was noted that in any attempt to model dark matter in galactic halos with classical fields will lead to anisotropic stresses comparable in magnitude with the energy density).…”

Section: Anisotropic Fluidmentioning

confidence: 99%

Averaging in spherically symmetric cosmology

Coley

Pelavas

2007

Phys. Rev. D

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The averaging problem in cosmology is of fundamental importance. When applied to study cosmological evolution, the theory of macroscopic gravity (MG) can be regarded as a long-distance modification of general relativity. In the MG approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We study the averaging problem within the class of spherically symmetric cosmological models. That is, we shall take the microscopic equations and effect the averaging procedure to determine the precise form of the correlation tensor in this case. In particular, by working in volume-preserving coordinates, we calculate the form of the correlation tensor under some reasonable assumptions on the form for the inhomogeneous gravitational field and matter distribution. We find that the correlation tensor in a Friedmann-Lemaître-Robertson-Walker (FLRW) background must be of the form of a spatial curvature. Inhomogeneities and spatial averaging, through this spatial curvature correction term, can have a very significant dynamical effect on the dynamics of the Universe and cosmological observations; in particular, we discuss whether spatial averaging might lead to a more conservative explanation of the observed acceleration of the Universe (without the introduction of exotic dark matter fields). We also find that the correlation tensor for a non-FLRW background can be interpreted as the sum of a spatial curvature and an anisotropic fluid. This may lead to interesting effects of averaging on astrophysical scales. We also discuss the results of averaging an inhomogeneous Lemaître-Tolman-Bondi solution as well as calculations of linear perturbations (that is, the backreaction) in an FLRW background, which support the main conclusions of the analysis.

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“…There were attempts at modelling the Kerr geometry [401], and generic “rotating” spacetimes [77], a proposal for using analogue models to generate massive phonon modes in BECs [400], and an extension of the usual formalism for representing weak-field gravitational lensing in terms of an analogue refractive index [38]. …”

Section: History and Motivationmentioning

confidence: 99%

Analogue Gravity

Barceló

Liberati

Visser

2005

Living Rev. Relativ.

Self Cite

958

992

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Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity).

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Effective refractive index tensor for weak-field gravity

Cited by 23 publications

References 17 publications

Averaging spherically symmetric spacetimes in general relativity

Averaging spherically symmetric spacetimes in general relativity

Averaging in spherically symmetric cosmology

Analogue Gravity

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