Hawking–Hayward quasi-local energy under conformal transformations

Prain, Angus; Vitagliano, Vincenzo; Faraoni, Valerio; Lapierre-Léonard, Marianne

doi:10.1088/0264-9381/33/14/145008

Cited by 26 publications

(29 citation statements)

References 43 publications

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“…The first method employs the transformation property of the Hawking-Hayward quasi-local mass under the conformal transformation of the spacetime metric g ab →g ab = Ω 2 g ab . The result is [45] M HH → M HH = Ã…”

Section: Hawking-hayward Mass In a Perturbed Flrw Cosmosmentioning

confidence: 99%

Turnaround size of non-spherical structures

Giusti

Faraoni

2019

Physics of the Dark Universe

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The turnaround radius of a large structure in an accelerating universe has been studied only for spherical structures, while real astronomical systems deviate from spherical symmetry. We show that, for small deviations from spherical symmetry, the gauge-invariant characterization of the turnaround size using the Hawking-Hayward quasi-local mass and spherical symmetry still applies, to first order in the cosmological perturbation potentials and in the deviations from sphericity. This is the first step to include non-spherical systems in the physics of turnaround. *

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Section: Hawking-hayward Mass In a Perturbed Flrw Cosmosmentioning

confidence: 99%

Turnaround size of non-spherical structures

Giusti

Faraoni

2019

Physics of the Dark Universe

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“…By comparing (29) and (31), one can identify that ω a as the variation of the symplectic Hamiltonian density where the boundary terms in both the equations are equivalent to each other as, √ −gΘ ′a (q, δq) ≡ p i (δx i ) and √ −gΘ ′a (q, £ ξ q) ≡ p i (d t x i ). Thus, with this above identification, the total variation of the Hamiltonian can be written as (using the Eq.…”

Section: Thermodynamic Quantities By Iyer-wald Formalism and Theimentioning

confidence: 99%

“…Although, the expression of the entropy and the temperature is widely accepted [20,21] to some extent but, there is a controversy in the expression of the energy which can be used for the thermodynamic description in this theory. Most of the existing expressions of energy (or mass) as described in literature are not conformally invariant [29][30][31], whereas, the expressions of the entropy and the temperature are conformally invariant. This makes the physicists more puzzled as none of the existing energy, so far, can be used together with entropy and temperature for the thermodynamic description.…”

Section: Introductionmentioning

confidence: 99%

Noether and Abbott-Deser-Tekin conserved quantities in scalar-tensor theory of gravity both in Jordan and Einstein frames

2018

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We revisit the thermodynamic aspects of the scalar-tensor theory of gravity in the Jordan and in the Einstein frame. Examining the missing links of this theory carefully, we establish the thermodynamic descriptions from the conserved currents and potentials by following both the Noether and the Abbott-Deser-Tekin (ADT) formalism. With the help of conserved Noether current and potential, we define the thermodynamic quantities, which we show to be conformally invariant. Moreover, the defined quantities are shown to fit nicely in the laws of (the first and the second) black hole thermodynamics formulated by the Wald's method. We stretch the study of the conformal equivalence of the physical quantities in these two frames by following the ADT formalism. Our further study reveals that there is a connection between the ADT and the Noether conserved quantities, which signifies that the ADT approach provide the equivalent thermodynamic description in the two frames as obtained in Noether prescription. Our whole analysis is very general as the conserved Noether and ADT currents and potentials are formulated off-shell and the analysis is exempted from any prior assumption or boundary condition.PACS numbers:

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“…it acquires the 'wrong' factor [17]. Given that the original Hawking-Hayward mass is of a purely geometric nature, it is no wonder that the latter would transform in a different way from the former.…”

Section: Resultsmentioning

confidence: 99%

Conformal mapping of the Misner–Sharp mass from gravitational collapse

Hammad

2016

Int. J. Mod. Phys. D

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The conformal transformation of the Misner-Sharp mass is reexamined. It has recently been found that this mass does not transform like usual masses do under conformal mappings of spacetime. We show that when it comes to conformal transformations, the widely used geometric definition of the Misner-Sharp mass is fundamentally different from the original conception of the latter. Indeed, when working within the full hydrodynamic setup that gave rise to that mass, i.e. the physics of gravitational collapse, the familiar conformal transformation of a usual mass is recovered. The case of scalar-tensor theories of gravity is also examined.

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Hawking–Hayward quasi-local energy under conformal transformations

Abstract: We derive a formula describing the transformation of the Hawking-Hayward quasi-local energy under a conformal rescaling of the spacetime metric. A known formula for the transformation of the Misner-Sharp-Hernandez mass is recovered as a special case.

Cited by 26 publications

References 43 publications

Turnaround size of non-spherical structures

Turnaround size of non-spherical structures

Noether and Abbott-Deser-Tekin conserved quantities in scalar-tensor theory of gravity both in Jordan and Einstein frames

Conformal mapping of the Misner–Sharp mass from gravitational collapse

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