Island in Charged Black Holes

TL;DR

This paper investigates the black hole information paradox using a doubly-holographic model with charged black holes, calculating entanglement entropy and Page curves, and exploring effects of backreaction and brane degrees of freedom.

Contribution

It introduces analytical and numerical methods to compute entanglement entropy and Page curves for charged black holes in a doubly-holographic framework, including backreaction effects.

Findings

Page curve with island on the brane is obtained.

Linear growth rate of entropy near extremality is found.

Strategies to ensure the paradox is well-described in the model are proposed.

Abstract

We study the information paradox for the eternal black hole with charges on a doubly-holographic model in general dimensions, where the charged black hole on a Planck brane is coupled to the baths on the conformal boundaries. In the case of weak tension, the brane can be treated as a probe such that its backreaction to the bulk is negligible. We analytically calculate the entanglement entropy of the radiation and obtain the Page curve with the presence of an island on the brane. For the near-extremal black holes, the growth rate is linear in the temperature. Taking both Dvali-Gabadadze-Porrati term and nonzero tension into account, we obtain the numerical solution with backreaction in four-dimensional spacetime and find the quantum extremal surface at $t=0$. To guarantee that a Page curve can be obtained in general cases, we propose two strategies to impose enough degrees of freedom on the brane such that the black hole information paradox can be properly described by the doubly-holographic setup.