Emissivities for the various Graviton Modes in the Background of the Higher-Dimensional Black Hole

Abstract

The Hawking emissivities for the scalar-, vector-, and tensor-mode bulk gravitons are computed in the full range of the graviton's energy by adopting the analytic continuation numerically when the spacetime background is $(4+n)$-dimensional non-rotating black hole. The total emissivity for the gravitons is only 5.16% of that for the spin-0 field when there is no extra dimension. However, this ratio factor increases rapidly when the extra dimensions exist. For example, this factor becomes 147.7%, 595.2% and 3496% when the number of extra dimensions is 1, 2 and 6, respectively. This fact indicates that the Hawking radiation for the graviton modes becomes more and more significant and dominant with increasing the number of extra dimensions.