Horizon Dynamics of a BTZ Black Hole

TL;DR

This paper models the horizon dynamics of a BTZ black hole using a membrane approach, translating it into a Klein-Gordon equation, quantizing solutions, and deriving quantum-corrected entropy consistent with the area law.

Contribution

It introduces a membrane-based framework for BTZ black hole horizons, deriving quantum corrections to entropy within a 1+1D Klein-Gordon formalism.

Findings

Quantum-corrected entropy matches the BTZ Bekenstein-Hawking law

Leading correction is proportional to the logarithm of the horizon area

Horizon dynamics can be effectively described by a quantized string model

Abstract

It has been suggested in the literature that, given a black hole spacetime, a relativistic membrane can provide an effective description of the horizon dynamics. In this paper, we explore such a framework in the context of a 2+1-dimensional BTZ black hole. Following this membrane prescription, we are able to translate the horizon dynamics (now described by a string) into the convenient form of a 1+1-dimensional Klein-Gordon equation. We proceed to quantize the solutions and construct a thermodynamic partition function. Ultimately, we are able to extract the quantum-corrected entropy, which is shown to comply with the BTZ form of the Bekenstein-Hawking area law. We also substantiate that the leading-order correction is proportional to the logarithm of the area.