Surface gravity in dynamical spherically symmetric spacetimes

G. Fodor, Kouji Nakamura, Yoshimi Oshiro, Akira Tomimatsu

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

A definition of surface gravity at the apparent horizon of dynamical spherically symmetric spacetimes is proposed. It is based on a unique foliation by ingoing null hypersurfaces. The function parametrizing the hypersurfaces can be interpreted as the phase of a light wave uniformly emitted by some far-away static observer. The definition gives back the accepted value of surface gravity in the static case by virtue of its nonlocal character. Although the definition is motivated by the behavior of outgoing null rays, it turns out that there is a simple connection between the surface gravity, the acceleration of any radially moving observer, and the observed frequency change of the infalling light signal. In particular, this gives a practical and simple method of how any geodesic observer can determine surface gravity by measuring only the redshift of the infalling light wave. The surface gravity can be expressed as an integral of matter field quantities along an ingoing null line, which shows that it is a continuous function along the apparent horizon. A formula for the area change of the apparent horizon is presented, and the possibility of thermodynamical interpretation is discussed. Finally, concrete expressions of surface gravity are given for a number of four-dimensional and two-dimensional dynamical black hole solutions.

Original languageEnglish
Pages (from-to)3882-3891
Number of pages10
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume54
Issue number6
Publication statusPublished - Sep 15 1996

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Gravity
Space-time
gravitation
horizon
Null
Observer
Horizon
Hypersurface
Foliation
Black Holes
Geodesic
Half line
rays
Continuous Function
Line

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)

Cite this

Surface gravity in dynamical spherically symmetric spacetimes. / Fodor, G.; Nakamura, Kouji; Oshiro, Yoshimi; Tomimatsu, Akira.

In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 54, No. 6, 15.09.1996, p. 3882-3891.

Research output: Contribution to journalArticle

Fodor, G. ; Nakamura, Kouji ; Oshiro, Yoshimi ; Tomimatsu, Akira. / Surface gravity in dynamical spherically symmetric spacetimes. In: Physical Review D - Particles, Fields, Gravitation and Cosmology. 1996 ; Vol. 54, No. 6. pp. 3882-3891.
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