Semiclassical Black Hole States and Entropy

TL;DR

This paper explores semiclassical quantum states of black holes, demonstrating how their entropy can be derived, matching Bekenstein-Hawking entropy for certain cases and revealing zero entropy for extremal Reissner-Nordström black holes.

Contribution

It establishes a link between reduced quantisation and Wheeler-DeWitt quantisation for black holes and computes their entropy within this framework.

Findings

Reproduces Bekenstein-Hawking entropy for Schwarzschild and non-extreme Reissner-Nordström black holes

Shows zero entropy for extremal Reissner-Nordström black holes

Connects reduced quantisation with Wheeler-DeWitt approach in quantum gravity

Abstract

We discuss semiclassical states in quantum gravity corresponding to Schwarzschild as well as Reissner Nordstr\"om black holes. We show that reduced quantisation of these models is equivalent to Wheeler-DeWitt quantisation with a particular factor ordering. We then demonstrate how the entropy of black holes can be consistently calculated from these states. While this leads to the Bekenstein-Hawking entropy in the Schwarzschild and non-extreme Reissner-Nordstr\"om cases, the entropy for the extreme Reissner-Nordstr\"om case turns out to be zero.