Bulk versus Brane in the Absorption and Emission : 5D Rotating Black Hole Case

TL;DR

This paper numerically analyzes the absorption and emission spectra of scalar fields around 5D rotating black holes, showing that superradiance effects are negligible for bulk scalars and confirming that black holes predominantly radiate on the brane.

Contribution

It provides a detailed numerical comparison of brane and bulk scalar field spectra in 5D rotating black holes, including superradiance effects, and confirms the dominance of brane radiation.

Findings

Low-energy absorption cross section equals horizon area.

Superradiance effect is negligible for bulk scalars.

Black holes mainly radiate on the brane despite superradiance.

Abstract

The absorption and emission spectra for the minimally-coupled brane and bulk scalar fields are numerically computed when the spacetime is a $5d$ rotating black hole carrying the two different angular momentum parameters $a$ and $b$. The effect of the superradiant scattering in the spectra is carefully examined. It is shown that the low-energy limit of the total absorption cross section always equal to the area of the non-spherically symmetric horizon, {\it i.e.} $4\pi (r_H^2 + a^2)$ for the brane scalar and $2\pi^2 (r_H^2 + a^2) (r_H^2 + b^2)/r_H$ for the bulk scalar where $r_H$ is an horizon radius. The energy amplification for the bulk scalar is roughly order of $10^{-9} %$ while that for the brane scalar is order of unity. This indicates that the effect of the superradiance is negligible for the case of the bulk scalar. Thus the standard claim that {\it black holes radiate mainly on the brane} is not changed although the effect of the superradiance is taken into account. The physical implication of this fac t is discussed in the context of TeV-scale gravity.