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

TL;DR

This paper demonstrates that higher-dimensional black holes emit Hawking radiation into the bulk that closely resembles perfect blackbody radiation, especially for large dimensions, due to frequency-independent greybody factors in the geometric-optics regime.

Contribution

It shows that for large extra dimensions, the emission spectrum of black holes can be accurately approximated by blackbody radiation, simplifying previous complex models.

Findings

Greybody factors become frequency-independent at large D.

Black hole emission spectrum approaches perfect blackbody form for D≫1.

Numerical results confirm analytical predictions.

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 $D$ ($3\leq D\lesssim10$), 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.