Bulk versus Brane Emissivities of Photon Fields: For the case of Higher-Dimensional Schwarzschild Phase

TL;DR

This paper compares photon emission spectra in higher-dimensional Schwarzschild spacetimes for bulk and brane scenarios, revealing that bulk emission becomes dominant with more extra dimensions, but the bulk-to-brane ratio per degree of freedom stays below one.

Contribution

It provides detailed calculations of photon emission spectra for both bulk and brane in higher dimensions, highlighting the dominance of bulk emission as the number of extra dimensions increases.

Findings

Vector mode emissivity surpasses scalar mode as extra dimensions grow.

Bulk emission becomes dominant over brane emission with increasing n.

Bulk-to-brane emissivity ratio per degree of freedom remains below one.

Abstract

The emission spectra for the spin-1 photon fields are computed when the spacetime is a $(4+n)$-dimensional Schwarzschild phase. For the case of the bulk emission we compute the spectra for the vector mode and scalar mode separately. Although the emissivities for the scalar mode is larger than those for the vector mode when $n$ is small, the emissivities for the vector mode photon become dominant rapidly with increasing $n$. For the case of the brane emission the emission spectra are numerically computed by making use of the complex potential method. Comparision of the total bulk emissivities with total brane emissivities indicates that the effect of the field spin makes the bulk emission to be rapidly dominant with increasing $n$. However, the bulk-to-brane relative emissivity per degree of freedom always remains smaller than unity. The importance for the spin-2 graviton emission problem is discussed.