On scalar curvature invariants in three dimensional spacetimes

Musoke, Nathan; McNutt, David; Coley, A. A.; Brooks, Daniel

doi:10.1007/s10714-016-2022-9

Cited by 3 publications

(1 citation statement)

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“…Refs. [138,139]). For completeness, an extension to our research would be to perturb these cosmologies and construct a ζ SMTP , or similar gauge invariant conserved quantity, which could be related to the perturbed matter content.…”

Section: Future Workmentioning

confidence: 99%

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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Section: Future Workmentioning

confidence: 99%

Conserved quantities in Lemaitre–Tolman–Bondi cosmology

Leithes

Malik

2014

Class. Quantum Grav.

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Asymptotic generalized extended uncertainty principle

Dąbrowski

Wagner

2020

Eur. Phys. J. C

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We present a formalism which allows for the perturbative derivation of the Extended Uncertainty Principle (EUP) for arbitrary spatial curvature models and observers. Entering the realm of small position uncertainties, we derive a general asymptotic EUP. The leading 2nd order curvature induced correction is proportional to the Ricci scalar, while the 4th order correction features the 0th order Cartan invariant $$\Psi _2$$Ψ2 (a scalar quadratic in curvature tensors) and the curved space Laplacian of the Ricci scalar all of which are evaluated at the expectation value of the position operator i.e. the expected position when performing a measurement. This result is first verified for previously derived homogeneous space models and then applied to other non-trivial curvature related effects such as inhomogeneities, rotation and an anisotropic stress fluid leading to black hole “hair”. Our main achievement combines the method we introduce with the Generalized Uncertainty Principle (GUP) by virtue of deformed commutators to formulate a generic form of what we call the Asymptotic Generalized Extended Uncertainty Principle (AGEUP).

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On the curvature invariants of the massive Banados–Teitelboim–Zanelli black holes and their holographic pictures

Ghodrati

Gregoris

2022

Int. J. Mod. Phys. A

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In this paper, the curvature structure of a ([Formula: see text])-dimensional black hole in the massive-charged-Born–Infeld gravity is investigated. The metric that we consider is characterized by four degrees of freedom which are the mass and electric charge of the black hole, the mass of the graviton field, and a cosmological constant. For the charged and neutral cases separately, we present various constraints among scalar polynomial curvature invariants which could invariantly characterize our desired space–times. Specially, an appropriate scalar polynomial curvature invariant and a Cartan curvature invariant which together could detect the black hole horizon would be explicitly constructed. Using algorithms related to the focusing properties of a bundle of light rays on the horizon which are accounted for by the Raychaudhuri equation, a procedure for isolating the black hole parameters, as the algebraic combinations involving the curvature invariants, would be presented. It will be shown that this technique could specially be applied for black holes with zero electric charge, contrary to the cases of solutions of lower-dimensional nonmassive gravity. In addition, for the case of massive ([Formula: see text])-dimensional black hole, the irreducible mass, which quantifies the maximum amount of energy which could be extracted from a black hole would be derived. Therefore, we show that the Hawking temperatures of these black holes could be reduced to the pure curvature properties of the space–times. Finally, we comment on the relationship between our analysis and the novel roles it could play in numerical quark–gluon plasma simulations and other QCD models and also black hole information paradox where the holographic correspondence could be exploited.

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On scalar curvature invariants in three dimensional spacetimes

Cited by 3 publications

References 35 publications

Conserved quantities in Lemaitre–Tolman–Bondi cosmology

Conserved quantities in Lemaitre–Tolman–Bondi cosmology

Asymptotic generalized extended uncertainty principle

On the curvature invariants of the massive Banados–Teitelboim–Zanelli black holes and their holographic pictures

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