Horizon quantization and thermodynamics of the 2+1 black hole

TL;DR

This paper applies a horizon quantization method to the 2+1 dimensional black hole, demonstrating it accurately predicts thermodynamic properties and deriving the horizon wave function's Schrödinger equation.

Contribution

It extends a previously proposed 4D horizon quantization approach to 2+1 dimensions, using string dynamics to describe horizon behavior.

Findings

Correctly reproduces the black hole's temperature and entropy

Derives the Schrödinger equation for the horizon wave function

Validates the quantization method in lower-dimensional black holes

Abstract

We test on the 2+1 dimensional black hole the quantization method that we have previously proposed in four dimensions. While in the latter case the horizon dynamics is described, at the effective level, by the action of a relativistic membrane, in the 2+1 case it is described by a string. We show that this approach reproduces the correct value of the temperature and entropy of the 2+1 dimensional black hole, and we write down the Schroedinger equation satisfied by the horizon wave function.