Bulk dominated fermion emission on a Schwarzschild background

TL;DR

This paper derives semi-analytic formulas for fermion absorption and emission rates on higher-dimensional Schwarzschild black holes, revealing bulk emission dominance in dimensions greater than five, challenging previous conjectures.

Contribution

It provides a general semi-analytic framework for fermion absorption and emission on spherically symmetric backgrounds in higher dimensions, extending previous numerical studies.

Findings

Bulk fermion emission dominates for dimensions greater than five.

Derived analytic relations between absorption probability and cross-section.

Emission rates are computed to third order in WKBJ approximation.

Abstract

Using the WKBJ approximation, and the Unruh method, we obtain semi-analytic expressions for the absorption probability (in all energy regimes) for Dirac fermions on a higher dimensional Schwarzschild background. We present an analytic expression relating the absorption probability to the absorption cross-section, and then use these results to plot the emission rates to third order in the WKBJ approximation. The set-up we use is sufficiently general such that it could also easily be applied to any spherically symmetric background in $d$-dimensions. Our results lead to the interesting conclusion that for $d>5$ bulk fermion emission dominates brane localised emission. This is an example contrary to the conjecture that black holes radiate mainly on the brane.