How the Change in Horizon Area Drives Black Hole Evaporation

Details How the Change in Horizon Area Drives Black Hole Evaporation How the Change in Horizon Area Drives Black Hole Evaporation

1999-03-08

arxiv.org/abs/gr-qc/9903027v2

Nucl.Phys. B575 (2000) 333-356

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

26 pages latex, extensively revised version of gr-qc/9801043. Definitive version to be published in Nucl. Phys. B

Scientific paper

10.1016/S0550-3213(00)00067-5

We rephrase the derivation of black hole radiation so as to take into account, at the level of transition amplitudes, the change of the geometry induced by the emission process. This enlarged description reveals that the dynamical variables which govern the emission are the horizon area and its conjugate time variable. Their conjugation is established through the boundary term at the horizon which must be added to the canonical action of general relativity in order to obtain a well defined action principle when the area varies. These coordinates have already been used by Teitelboim and collaborators to compute the partition function of a black hole. We use them to show that the probability to emit a particle is given by $e^{- \Delta A/4}$ where $\Delta A$ is the decrease in horizon area induced by the emission. This expression improves Hawking result which is governed by a temperature (given by the surface gravity) in that the specific heat of the black hole is no longer neglected. The present derivation of quantum black hole radiation is based on the same principles which are used to derive the first law of classical black hole thermodynamics. Moreover it also applies to quantum processes associated with cosmological or acceleration horizons. These two results indicate that not only black holes but all event horizons possess an entropy which governs processes according to quantum statistical thermodynamics.

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