Lemaître model and cosmic mass

International audienceNumerical studies of gravitational collapse to black holes make use of apparent horizons, which are intrinsically foliation dependent. We expose the problem and discuss possible solutions using the Hawking-Hayward quasilocal mass. In spherical symmetry, we present a physically sensible approach to the problem by restricting to spherically symmetric spacetime slicings. In spherical symmetry, the apparent horizons enjoy a restricted gauge independence in any spherically symmetric foliation, but physical quantities associated with them, such as surface gravity and temperature, are fully gauge dependent. The widely used comoving and Kodama foliations, which are of particular interest, are discussed in detail as examples

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“…we have at the horizon 20) which is expected since, again, the Kodama observer is null at the horizon. However the relative velocity v…”

Section: Relation Between Comoving and Kodama Gaugesmentioning

confidence: 52%

“…We refer to black hole apparent horizons but most of our considerations apply to cosmological apparent horizons as well 4. The Misner-Sharp-Hernandez mass is also used for cosmological black holes[19,7] and coincides with the Lemaître mass used in Lemaître-Tolman-Bondi geometries[20].…”

mentioning

confidence: 99%

Foliation dependence of black hole apparent horizons in spherical symmetry

et al. 2017

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“…In addition, further extensions of this research into similar and related spacetimes, such as Lemaître, may provide similar tools for comparing inhomogeneous spacetimes with the standard FRW model, as was highlighted with reference to our research in Ref. [117]. This is of particular interest to research trying to explain the effects of Dark Energy using inhomogeneous spacetimes.…”

Section: Discussion On Gauge-invariants In Inhomogeneous Spacetimesmentioning

confidence: 60%

Conserved quantities in Lemaitre–Tolman–Bondi cosmology

Leithes

Malik

2014

Class. Quantum Grav.

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We study linear perturbations to a Lemaître-Tolman-Bondi (LTB) background spacetime. Studying the transformation behaviour of the perturbations under gauge transformations, we construct gauge invariant quantities. We show, using the perturbed energy conservation equation, that there are conserved quantities in LTB, in particular a spatial metric trace perturbation, ζSMTP, which is conserved on all scales. We then briefly extend our discussion to the Lemaître spacetime, and construct gauge-invariant perturbations in this extension of LTB spacetime. I. INTRODUCTIONConserved quantities are useful tools with a wide range of applications in cosmology. In particular, they allow us to relate early and late times in a cosmological model, without explicitly having to solve the evolution equations, either exactly or taking advantage of some limiting behaviour. These quantities have been studied extensively within the context of cosmological perturbation theory, and usually applied to a Friedmann-Robertson-Walker(FRW) background spacetime.Using metric based cosmological perturbation theory [1, 2], we can readily construct gauge-invariant quantities which are also conserved, that is constant in time (see e.g. Ref.[3] for early work on this topic). In a FRW background spacetime, ζ, the curvature perturbation on uniform density hypersurfaces, is conserved on large scales for adiabatic fluids. To show that ζ is conserved and under what conditions, we only need the conservation of energy [4]. This was first shown to work for fluids at linear order, but it holds also at second order in the perturbations, and in the fully non-linear case, usually referred to as the δN formalism [4-6] 1 .Instead of, or in addition to, cosmological perturbation theory, we can also use other approximation schemes to deal with the non-linearity of the Einstein equations. In particular gradient expansion schemes have proven to be useful in the context of conserved quantities, again with the main focus on FRW spacetimes [6][7][8][9]. But conserved quantities have also been studied for spacetimes other than FRW, such as braneworld models (see e.g. Ref.[10], and anisotropic spacetime (e.g. Ref. [11]).The Lemaître-Tolman-Bondi (LTB) spacetime [12] is a more general solution to Einstein's field equations than the Friedmann-Robertson-Walker (FRW) model. While LTB is invariant under rotations, FRW is rotation and translations invariant, and hence has homogeneous and isotropic, maximally symmetric spatial sections [13].Recent research into LTB cosmology has been motivated by seeking an alternative explanation for the late time accelerated expansion of the universe, as indicated by e.g. SNIa observations [14]. Inhomogeneous cosmologies, including LTB, have been suggested as such an alternative explanation of these observations (see e.g. Refs. [15,16]). Other observations such as galaxy surveys, large scale structure surveys, the CMB and indeed any redshift dependent observations (see for example Refs. [17], [18], [19]) are usually interpreted assuming a flat FR...

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“…Through a straightforward change of coordinates (see ref. [94]), one can recast the metric (2.3) into the form…”

Section: Basic Features Of the Misner-sharp Massmentioning

confidence: 99%

Quasi-local masses and cosmological coupling of black holes and mimickers

Cadoni,

Murgia,

Pitzalis

et al. 2024

J. Cosmol. Astropart. Phys.

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Motivated by the recent heated debate on whether the masses of local objects, such as compact stars or black holes (BHs), may be affected by the large-scale, cosmological dynamics, we analyze the conditions under which, in a general relativity framework, such a coupling small/large scales is allowed. We shed light on some controversial arguments, which have been used to rule out the latter possibility. We find that the cosmological coupling occurs whenever the energy of the central objects is quantified by the quasi-local Misner-Sharp mass (MS). Conversely, the decoupling occurs whenever the MS mass is fully equivalent to the (nonlocal) Arnowitt-Deser-Misner (ADM) mass. Consequently, for singular BHs embedded in cosmological backgrounds, like the Schwarzschild-de Sitter or McVittie solutions, we show that there is no cosmological coupling, confirming previous results in the literature. Furthermore, we show that nonsingular compact objects couple to the cosmological background, as quantified by their MS mass. We conclude that observational evidence of cosmological coupling of astrophysical BHs would be the smoking gun of their nonsingular nature.

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Lemaître model and cosmic mass

Abstract: The mass of a sphere of simmetry in the Lemaître universe is discussed using the Hawking-Hayward quasi-local energy and clarifying existing ambiguities. A covariantly conserved current introduced by Cahill and McVittie is shown to be a multiple of the Kodama energy current.

Cited by 4 publications

References 35 publications

Foliation dependence of black hole apparent horizons in spherical symmetry

Foliation dependence of black hole apparent horizons in spherical symmetry

Conserved quantities in Lemaitre–Tolman–Bondi cosmology

Quasi-local masses and cosmological coupling of black holes and mimickers

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