Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-07-05
Class.Quant.Grav.28:105016,2011
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
5 pages
Scientific paper
10.1088/0264-9381/28/10/105016
We study the Hawking radiation emitted into the bulk by $(D+1)$-dimensional Schwarzschild black holes. It is well-known that the black-hole spectrum departs from exact blackbody form due to the frequency dependence of the `greybody' factors. For intermediate values of $D$ ($3\leq D\lesssim10$), these frequency-dependent factors may significantly modify the spectrum of the emitted radiation. However, we point out that for $D\gg1$, the typical wavelengths in the black-hole spectrum are much {\it shorter} than the size of the black hole. In this regime, the greybody factors are well described by the geometric-optics approximation according to which they are almost frequency-independent. Following this observation, we argue that for higher-dimensional black holes with $D\gg1$, the total power emitted into the bulk should be well approximated by the analytical formula for perfect blackbody radiation. We test the validity of this analytical prediction with numerical computations.
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