Low-Energy Absorption Cross Section for massive scalar and Dirac fermion by $(4+n)$-dimensional Schwarzschild Black Hole

TL;DR

This paper calculates low-energy absorption cross sections for massive scalars and Dirac fermions around higher-dimensional Schwarzschild black holes, revealing how extra dimensions influence absorption properties in brane-world scenarios.

Contribution

It introduces a direct method to compute partial absorption cross sections for massive Dirac fermions with spin in higher dimensions, extending previous results and highlighting the impact of extra dimensions.

Findings

Low $ ext{l}$-level contributions dominate in the massive case.

The ratio of absorption cross sections depends on the number of extra dimensions.

The bulk scalar cross section matches the horizon area in the massless limit.

Abstract

Motivated by the brane-world scenarios, we study the absorption problem when the spacetime background is $(4+n)$-dimensional Schwarzschild black hole. We compute the low-energy absorption cross sections for the brane-localized massive scalar, brane-localized massive Dirac fermion, and massive bulk scalar. For the case of brane-localized massive Dirac fermion we introduce the particle's spin in the traditional Dirac form without invoking the Newman-Penrose method. Our direct introduction of spin enables us to compute contributions to the $j$th-level partial absorption cross section from orbital angular momenta $\ell = j \pm 1/2$. It is shown that the contribution from the low $\ell$-level is larger than that from the high $\ell$-level in the massive case. In the massless case these two contributions are exactly same with each other. The ratio of low-energy absorption cross sections for Dirac fermion and for scalar is dependent on the number of extra dimensions as $2^{(n-3)/ (n+1)}$. Thus the ratio factor 1/8 is recovered when $n=0$, which Unruh found. The physical importance of this ratio factor is discussed in the context of the brane-world scenario. For the case of bulk scalar our low-energy absorption cross section for S-wave is exactly same with area of the horizon hypersurface in the massless limt, which is an higher-dimensional generaliztion of universality. Our results for all cases turn out to have correct massless and 4d limits.