### 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 language | English |
---|---|

Pages (from-to) | 3882-3891 |

Number of pages | 10 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 54 |

Issue number | 6 |

Publication status | Published - Sep 15 1996 |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*54*(6), 3882-3891.

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

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 54, no. 6, pp. 3882-3891.

}

TY - JOUR

T1 - Surface gravity in dynamical spherically symmetric spacetimes

AU - Fodor, G.

AU - Nakamura, Kouji

AU - Oshiro, Yoshimi

AU - Tomimatsu, Akira

PY - 1996/9/15

Y1 - 1996/9/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0040488839&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040488839&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0040488839

VL - 54

SP - 3882

EP - 3891

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 6

ER -