Graviton Emission in the Bulk from a Higher-Dimensional Schwarzschild Black Hole

TL;DR

This paper analyzes graviton emission from higher-dimensional Schwarzschild black holes, providing analytical solutions for the emission rates in the low-energy regime and revealing a vector radiation dominance.

Contribution

It offers the first analytical calculation of graviton emission rates in the bulk for all perturbation types in higher dimensions, highlighting the dominance of vector radiation.

Findings

Vector radiation dominates for all n.

Low-energy graviton emission is below scalar emission due to mode absence.

Emission rate decreases with increasing n at low energies.

Abstract

We consider the evaporation of (4+n)-dimensional non-rotating black holes into gravitons. We calculate the energy emission rate for gravitons in the bulk obtaining analytical solutions of the master equation satisfied by all three types (S,V,T) of gravitational perturbations. Our results, valid in the low-energy regime, show a vector radiation dominance for every value of n, while the relative magnitude of the energy emission rate of the subdominant scalar and tensor radiation depends on n. The low-energy emission rate in the bulk for gravitons is well below that for a scalar field, due to the absence of the dominant l=0,1 modes from the gravitational spectrum. Higher partial waves though may modify this behaviour at higher energies. The calculated low-energy emission rate, for all types of degrees of freedom decreases with n, although the full energy emission rate, integrated over all frequencies, is expected to increase with n, as in the previously studied case of a bulk scalar field.