Gravitational energy in spherical symmetry

Hayward, Sean A.

doi:10.1103/physrevd.53.1938

Cited by 485 publications

(721 citation statements)

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“…It would be preferable to have independently motivated definitions of these quantities, but so far this has been done only in spherical symmetry [19,20,21], where there are natural definitions of E, κ and Φ = Q/R which can be applied anywhere in the space-time, coinciding with the above expressions on the outer horizons of a ReissnerNordström black hole. In the dynamical context, E ≥ M is generally not the ADM energy, since there may be matter or gravitational radiation outside the black hole.…”

Section: State Spacementioning

confidence: 99%

“…So a black hole grows if something falls into it, otherwise staying the same size. Comprehensive treatments were subsequently given for spherical symmetry [19,20,21], cylindrical symmetry [22] and a quasi-spherical approximation [23,24,25,26]. In each case, definitions were found for all the non-zero physical quantities mentioned above, providing prototypes of all except J and Ω.…”

Section: Introductionmentioning

confidence: 99%

“…A unified framework for any trapping horizon is provided by a dual-null formalism [44,45], which was used throughout the earlier studies [18,19,20,21,22,23,24,25,26]. The energy flux equation was then cast in a surface-integral form where the null limit could be taken [46,47].…”

Section: Introductionmentioning

confidence: 99%

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Angular momentum conservation for dynamical black holes

Hayward

2006

Phys. Rev. D

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Angular momentum can be defined by rearranging the Komar surface integral in terms of a twist form, encoding the twisting around of space-time due to a rotating mass, and an axial vector. If the axial vector is a coordinate vector and has vanishing transverse divergence, it can be uniquely specified under certain generic conditions. Along a trapping horizon, a conservation law expresses the rate of change of angular momentum of a general black hole in terms of angular momentum densities of matter and gravitational radiation. This identifies the transverse-normal block of an effective gravitational-radiation energy tensor, whose normal-normal block was recently identified in a corresponding energy conservation law. Angular momentum and energy are dual respectively to the axial vector and a previously identified vector, the conservation equations taking the same form. Including charge conservation, the three conserved quantities yield definitions of an effective energy, electric potential, angular velocity and surface gravity, satisfying a dynamical version of the so-called first law of black-hole mechanics. A corresponding zeroth law holds for null trapping horizons, resolving an ambiguity in taking the null limit.

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Section: State Spacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Angular momentum conservation for dynamical black holes

Hayward

2006

Phys. Rev. D

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“…This is a well-behaved quasi-local mass in spherically symmetric spacetimes [7], which can be written as…”

Section: B Misner-sharp Mass and Trapping Horizonsmentioning

confidence: 99%

“…In this paper, we adopt the "trapping horizon" framework introduced by Hayward [7,8] because this provides a systematic and mathematically transparent view of the sort of cosmological black holes treated here. In the context of this paper, trapping horizons and conventional apparent horizons are almost equivalent but they need not be in more general situations.…”

Section: B Misner-sharp Mass and Trapping Horizonsmentioning

confidence: 99%

Super-horizon primordial black holes

Harada

Carr

2005

Phys. Rev. D

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We discuss a new class of solutions to the Einstein equations which describe a primordial black hole (PBH) in a flat Friedmann background. Such solutions arise if a Schwarzschild black hole is patched onto a Friedmann background via a transition region. They are possible providing the black hole event horizon is larger than the cosmological apparent horizon. Such solutions have a number of strange features. In particular, one has to define the black hole and cosmological horizons carefully and one then finds that the mass contained within the black hole event horizon decreases when it is larger than the Friedmann cosmological apparent horizon, although its area always increases. These solutions involve two distinct future null infinities and are interpreted as the conversion of a white hole into a black hole. Although such solutions may not form from gravitational collapse in the same way as standard PBHs, there is nothing unphysical about them, since all energy and causality conditions are satisfied. Their conformal diagram is a natural amalgamation of the Kruskal diagram for the extended Schwarzschild solution and the conformal diagram for a black hole in a flat Friedmann background. In this paper, such solutions are obtained numerically for a spherically symmetric universe containing a massless scalar field, but it is likely that they exist for more general matter fields and less symmetric systems.

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Some remarks on the Bel-Robinson tensor

Garecki¹

2001

Ann. Phys.

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In this paper we present our point of view on the correct physical interpretation of the Bel-Robinson tensor within the framework of standard General Relativity (GR), i.e., within the framework of GR without supplementary elements like an arbitrary vector field, a distinguished tetrad field or a second metric. We show that this tensor arises as a consequence of the Bianchi identities and, in a natural manner, it is linked to the difference of the canonical gravitational energy-momentum as calculated in normal coordinates in a small vicinity of their origin P and in the origin P.

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Gravitational energy in spherical symmetry

Cited by 485 publications

References 50 publications

Angular momentum conservation for dynamical black holes

Angular momentum conservation for dynamical black holes

Super-horizon primordial black holes

Some remarks on the Bel-Robinson tensor

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