Bulk emission by higher-dimensional black holes: almost perfect blackbody radiation

Abstract

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 ⩽ D ≲10), these frequency-dependent factors may significantly modify the spectrum of the emitted radiation. However, we point out that for D ≫ 1, the typical wavelengths in the black-hole spectrum are much 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 ≫ 1, 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.