Probability distribution for black hole evaporation

Abstract

Nonthermal correction to the emission probability of particles from black holes can be obtained if the backreaction or self-gravitational effects of the emitted particles on the black hole spacetime are taken into consideration. These nonthermally emitted particles conserve the entropy of the black hole---i.e., the entropy of the system of radiated particles after complete evaporation of the black hole matches the initial entropy of the black hole. Using the nonthermal emission probability, we have determined the probability for a black hole of mass $M$ to be completely evaporated by a given number of particles $n$. This is done by first evaluating the number of possible ways in which the black hole can be evaporated by emitting $n$ number of particles, and then the total number of ways in which the black hole can be evaporated. The ratio of these two quantities gives us the desired probability. From the probability distribution, we get a displacement relation between the most probable number of particles exhausting the black hole and the temperature of the initial black hole. This relation resembles Wien's displacement law for blackbody radiation.