Page Curves of Reissner-Nordstr\"om Black Hole in HD Gravity

TL;DR

This paper computes the Page curves for Reissner-Nordström black holes in four-dimensional higher derivative gravity theories, showing how entanglement entropy evolves over time and depends on the gravitational corrections, with implications for black hole information.

Contribution

It derives the Page curves for charged black holes in higher derivative gravity theories, analyzing the effects of ${ m O}(R^2)$ and Gauss-Bonnet terms on entanglement entropy and scrambling time.

Findings

Page curves reach a constant value after the Page time.

Gauss-Bonnet coupling affects the timing of Page curve appearance.

Scrambling time varies with ${ m O}(R^2)$ corrections, but not with Gauss-Bonnet terms.

Abstract

We obtain the Page curves of an eternal Reissner-Nordstr\"om black hole in the presence of higher derivative terms in four dimensions. We consider two cases: gravitational action with general ${\cal O}(R^2)$ terms plus Maxwell term and Einstein-Gauss-Bonnet gravity plus Maxwell term. In both the cases entanglement entropy of the Hawking radiation in the absence of island surface is increasing linearly with time. After including contribution from the island surface, we find that after the Page time, entanglement entropy of the Hawking radiation in both the cases reaches a constant value which is the twice of the Bekenstein-Hawking entropy of the black hole and we obtain the Page curves. We find that Page curves appear at later or earlier time when the Gauss-Bonnet coupling increases or decreases. Further, scrambling time of Reissner-Nordstr\"om is increasing or decreasing depending upon whether the correction term (coming from ${\cal O}(R^2)$ terms in the gravitational action) is increasing or decreasing in the first case whereas scrambling time remains unaffected in the second case (Einstein-Gauss-Bonnet gravity case). As a consistency check, in the limit of vanishing GB coupling we obtain the Page curve of the Reissner-Nordstr\"om black hole obtained in arXiv:2101.06867.