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Cited by 493

The DOI matches its Crossref record; 48 of the 48 references it cites were found in a registry or an index.

Gravitational energy in spherical symmetry

Open access
Hayward, Sean A.·1996·Physical Review D
DOI 10.1103/physrevd.53.1938
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Abstract

Various properties of the Misner-Sharp spherically symmetric gravitational energy E are established or reviewed. In the Newtonian limit of a perfect fluid, E yields the Newtonian mass to leading order and the Newtonian kinetic and potential energy to the next order. For test particles, the corresponding H\'aj\'{\i}\ifmmode \check{c}\else \v{c}\fi{}ek energy is conserved and has the behavior appropriate to energy in the Newtonian and special-relativistic limits. In the small-sphere limit, the leading term in E is the product of volume and the energy density of the matter. In vacuo, E reduces to the Schwarzschild energy. At null and spatial infinity, E reduces to the Bondi-Sachs and Arnowitt-Deser-Misner energies, respectively. The conserved Kodama current has charge E. A sphere is trapped if E>1/2r, marginal if E=1/2r, and untrapped if E1/2r, where r is the areal radius. A central singularity is spatial and trapped if E>0, and temporal and untrapped if E0. On an untrapped sphere, E is nondecreasing in any outgoing spatial or null direction, assuming the dominant energy condition. It follows that E\ensuremath{\ge}0 on an untrapped spatial hypersurface with a regular center, and E\ensuremath{\ge}1/2${\mathit{r}}_{0}$ on an untrapped spatial hypersurface bounded at the inward end by a marginal sphere of radius ${\mathit{r}}_{0}$. All these inequalities extend to the asymptotic energies, recovering the Bondi-Sachs energy loss and the positivity of the asymptotic energies, as well as proving the conjectured Penrose inequality for black or white holes. Implications for the cosmic censorship hypothesis and for general definitions of gravitational energy are discussed. \textcopyright{} 1996 The American Physical Society.

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Metadata

Authors
Hayward, S. A.
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
1996-02-15
Volume
53
Issue
4
Pages
1938-1949
ISSN
  • 0556-2821 (ISSN-L)
  • 1089-4918
DOI
10.1103/physrevd.53.1938
OpenAlex
W1996146431
Cited by
493
References
48
FWCI
5.80
Type
journal article
Language
en
Open access
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