Schwarzschild black holes, Islands and Virasoro algebra

TL;DR

This paper investigates the entanglement entropy of Schwarzschild black holes as their mass approaches zero, proposing a bound involving the Virasoro algebra's central charge to resolve entropy explosion issues and deriving a Page curve without islands.

Contribution

It introduces a novel bound c < A*M linking central charge and black hole mass to address entropy divergence and explores entropy calculations with and without islands.

Findings

Bound c < A*M prevents entropy explosion at small masses.

A mechanism based on variable central charge reproduces the Page curve.

Entropy remains finite as black hole mass approaches zero.

Abstract

The Schwarzschild black hole metric with mass $M$ has the limit of the vanishing mass when one get the Minkowski space. We study behavior of the entanglement entropy by using the island formula and the limit of the vanishing black hole mass. The black hole information problem appears if one considers the lowering its mass. It was noted recently that the formula derived for eternal black holes leads to an increase of the entanglement entropy, which is singular when $M \to 0$. In this process, it arises the other problem of the Schwarzschild black hole explosion, as the black hole temperature blows up as the mass vanishes.We show that it is possible to solve the entropy explosion for small masses, if one admit the following bound: $c<AM$ where $c$ is central charge of the Virasoro algebra, M is black hole mass and A is positive constant. We are examining the possibilities of applying such a mechanism to calculate entropy with and without an island. It was shown that applying the mechanism of the dependence of the central charge on the black hole mass allows us to obtain a similar Page curve without using an island.