Partition Function of the Reissner-Nordstr\"om Black Hole

TL;DR

This paper develops a microscopic model of a Reissner-Nordström black hole's stretched horizon, deriving an explicit partition function that explains Hawking radiation and entropy through phase transitions at the horizon.

Contribution

It introduces a discrete constituent model for the black hole horizon and derives an explicit partition function, providing a microscopic explanation for Hawking radiation and entropy.

Findings

Partition function derived explicitly for Reissner-Nordström black hole

Hawking effect explained as a phase transition at the horizon

Reproduces Bekenstein-Hawking entropy law

Abstract

We consider a microscopic model of a stretched horizon of the Reissner-Nordstr\"om black hole. In our model the stretched horizon consists of discrete constituents. Using our model we obtain an explicit, analytic expression for the partition function of the hole. Our partition function implies, among other things, the Hawking effect, and provides it with a microscopic explanation as a phase transition taking place at the stretched horizon. The partition function also implies the Bekenstein-Hawking entropy law. The model and its consequences are similar to those obtained previously for the Schwarzschild black hole.