The effect of R\xe9nyi entropy on Hawking radiation

Abstract

It is widely believed that Hawking radiation originates from excitations near the horizons of black holes (Hawking in Commun Math Phys 43:199, 1975, Giddings in Phys Lett B 754:39, 2016, Mathur in Class Quantum Gravity 26:224001, 2009). However, Giddings (Phys Lett B 754:39, 2016) proposed that the Hawking radiation spectrum that characterizes evaporating semi-classical black holes originates from a quantum “atmosphere”, which extends beyond the horizon of a black hole. Although several research projects have been conducted in this field, they have not yet taken into account the effect of Rényi entropy. In the present article, we will therefore consider the effect of Rényi entropy on Hawking radiation power. We assume that if the effect of Rényi entropy is very small, we suggest that the Hawking radiation should originate from the quantum “atmosphere” which extends beyond the black hole’s horizon for finite dimensions. That is, that Giddings’ suggestion is the more likely of the above possibilities. However, for infinite dimensions, both suggestions are equally credible. We briefly consider the very large effect of Rényi entropy on Hawking radiation power as well. We find that if the effect of Rényi entropy is very large and omega /T_{BH} is very small, then the power spectral density S_R is proportional to the power spectral density S_{BH}.