Low-Energy Absorption Cross Section for massive scalar and Dirac fermion by (4+n)-dimensional Schwarzschild Black Hole
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TL;DR: In this article, the authors studied the absorption problem when the spacetime background is (4+n)-dimensional Schwarzschild black hole and derived the low-energy absorption cross-sections for the brane-localized massive Dirac fermion, massive scalar, and massive bulk scalar.
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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 jth-level partial absorption cross section from orbital angular momenta l = j±1/2. It is shown that the contribution from the low l-level is larger than that from the high l-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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Citations
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