Generalized Hawking radiation power corresponding to Sharma–Mittal entropy

Abstract

The effective radius of the black hole radiation as $r_A$, determines the area in space–time around the black hole with radius $r_{BH}$, which is the source of the black hole’s Hawking radiation. Also here, it should be noted that, the effective radius as a geometric bound of a specific area around the black hole plays an important role in understanding the thermodynamics of the black hole. The general belief based on Hawking’s opinion was that $r_A\sim r_{BH}$ but Giddings concluded that $r_A\sim 2r_{BH}$. On the other hand, many researches have shown that the generalized entropies for the describing gravitational phenomena more appropriate than the Boltzmann–Gibbs entropy. Among the generalized entropies, we can mention Tsallis, Renyi and Sharma–Mittal entropies. Generally one can say that the Sharma–Mittal entropy can be converted into Tsallis and Renyi entropies under certain conditions. Therefore, the question that arises here is that, by changing surface entropy of black hole to Sharma–Mittal entropy, how will be compatible the effective radius of the black hole with Hawking’s and Gidding’s point of view ? Or how is changed the effective radius by changing the surface entropy of black hole? Our main motivation for presenting this paper is that we have to give answer the above mentioned question.