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

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

2004-06-14

arxiv.org/abs/hep-th/0406117v2

JHEP0409:005,2004

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, 1 postscript figure, v2: computational mistakes are corrected

Scientific paper

10.1088/1126-6708/2004/09/005

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.

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