Page curves of Reissner-Nordstrom black hole in HD gravity

We obtain the Page curves of an eternal Reissner-Nordstrom black hole in the presence of higher derivative terms in four dimensions. We consider two cases: gravitational action with general 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-Nordstrom is increasing or decreasing depending upon whether the correction term (coming from 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-Nordstrom black hole obtained in Wang et al. (JHEP 04:103, 2021).

Automated summary

We studied the Page curves of an eternal Reissner-Nordstrom black hole in four dimensions with the presence of higher derivative terms. We found that adding contribution from the island surface led to a constant value of entanglement entropy of the Hawking radiation, which is twice of the Bekenstein-Hawking entropy of the black hole.