On the Gravitational Back Reaction to Hawking Radiation

Details On the Gravitational Back Reaction to Hawking Radiation On the Gravitational Back Reaction to Hawking Radiation

1998-01-13

arxiv.org/abs/gr-qc/9801043v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, latex

Scientific paper

We show that a surface term should be added to the Einstein-Hilbert action in order to properly describe quantum transitions occurring around a black hole. The introduction of this boundary term has been advocated by Teitelboim and collaborators and it has been used in the computation of the black hole entropy. Here, we use it to compute the gravitational corrections to the transition amplitudes giving rise to Hawking radiation. This surface term implies that the probability to emit a particle is given by $e^{- \Delta A/4}$ where $\Delta A$ is the change in the area of the black hole horizon induced by the emission. Its inclusion at the level of the amplitudes therefore relates quantum black hole radiation to the first law of black hole dynamics. In both cases indeed, the term expressing the change in area directly results from the same boundary term introduced for the same reason: to obtain a well defined action principle.

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