Schwarzschild black holes, Islands and Virasoro algebra

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.

References in corpus (8)

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• The Page curve of Hawking radiation from semiclassical geometry
• Islands in Schwarzschild black holes
• Islands and Page curves of Reissner-Nordström black holes
• The universality of islands outside the horizon
• Entanglement entropy of asymptotically flat non-extremal and extremal black holes with an island
• Microfield Dynamics of Black Holes
• Entanglement entropy of near-extremal black hole