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

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 branelocalized 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 as Unruh found long ago. 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 ∗Email:[email protected] †Email:[email protected] ‡Email:[email protected] 1 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.