Finiteness of Entanglement Entropy in Quantum Black Hole

TL;DR

This paper proposes a modified entanglement entropy formula for black holes that removes divergence issues, linking it to quantum corrections, Rènyi entropy, and higher spin black holes, advancing understanding of black hole quantum properties.

Contribution

It introduces a new form of black hole entanglement entropy that cures divergence problems and explores its implications for quantum corrections and advanced black hole models.

Findings

Divergence in entanglement entropy is resolved by the proposed modification.

The modified entropy relates to Rènyi entropy and higher quantum corrections.

Implications for the final black hole stage and higher spin black holes are discussed.

Abstract

A logarithmic but divergent term usually appears in the computation of entanglement entropy circumferencing a black hole, while the leading quantum correction to the Bekenstein-Hawking entropy also takes the logarithmic form. A quench model of CFT within finite Euclidean time was proposed in the \cite{Kuwakino:2014nra} to regard this logarithmic term as entanglement between radiation and the black hole, and this proposal was justified by the alternative sign for $n$-partite quantum information. However, this preliminary form suffers from the notorious divergence at its low temperature limit. In this letter, we propose a modified form for black hole entanglement entropy such that the divergence sickness can be cured. We discuss the final stage of black hole due to this modification and its relation to R{\`e}nyi entropy, higher loop quantum correction and higher spin black holes.