Absorption and Emission Spectra of an higher-dimensional Reissner-Nordström black hole

Abstract

The absorption and emission problems of the brane-localized and bulk scalars are examined when the spacetime is a $(4+n)$-dimensional Reissner-Nordström black hole. Making use of an appropriate analytic continuation, we compute the absorption and emission spectra in the full range of particle's energy. For the case of the brane-localized scalar the presence of the nonzero inner horizon parameter $r_-$ generally enhances the absorptivity and suppresses the emission rate compared to the case of the Schwarzschild phase. The low-energy absorption cross section exactly equals to $4πr_+^2$, two-dimensional horizon area. The effect of the extra dimensions generally suppresses the absorptivity and enhances the emission rate, which results in the disappearance of the oscillatory pattern in the total absorption cross section when $n$ is large. For the case of the bulk scalar the effect of $r_-$ on the spectra is similar to that in the case of the brane-localized scalar. The low-energy absorption cross section equals to the area of the horizon hypersurface. In the presence of the extra dimensions the total absorption cross section tends to be inclined with a positive slope. It turns out that the ratio of the {\it missing} energy over the {\it visible} one decreases with increase of $r_-$.