Page curves of Reissner–Nordström black hole in HD gravity

Gopal Yadav (Department of Physics, Indian Institute of Technology Roorkee, Roorkee, 247667, India)

We obtain the Page curves of an eternal Reissner–Nordström black hole in the presence of higher derivative terms in four dimensions. We consider two cases: gravitational action with general $${\mathcal {O}}(R^2)$$ 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–Nordström is increasing or decreasing depending upon whether the correction term (coming from $${\mathcal {O}}(R^2)$$ 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–Nordström black hole obtained in Wang et al. (JHEP 04:103, 2021).

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      "source": "Springer", 
      "value": "We obtain the Page curves of an eternal Reissner\u2013Nordstr\u00f6m black hole in the presence of higher derivative terms in four dimensions. We consider two cases: gravitational action with general  $${\\mathcal {O}}(R^2)$$  <math> <mrow> <mi>O</mi> <mo>(</mo> <msup> <mi>R</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </math>   terms plus Maxwell term and Einstein\u2013Gauss\u2013Bonnet 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\u2013Hawking 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\u2013Bonnet coupling increases or decreases. Further, scrambling time of Reissner\u2013Nordstr\u00f6m is increasing or decreasing depending upon whether the correction term (coming from  $${\\mathcal {O}}(R^2)$$  <math> <mrow> <mi>O</mi> <mo>(</mo> <msup> <mi>R</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </math>   terms in the gravitational action) is increasing or decreasing in the first case whereas scrambling time remains unaffected in the second case (Einstein\u2013Gauss\u2013Bonnet gravity case). As a consistency check, in the limit of vanishing GB coupling we obtain the Page curve of the Reissner\u2013Nordstr\u00f6m black hole obtained in Wang et al. (JHEP 04:103, 2021)."
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Published on:
12 October 2022
Publisher:
Springer
Published in:
European Physical Journal C , Volume 82 (2022)
Issue 10
Pages 1-15
DOI:
https://doi.org/10.1140/epjc/s10052-022-10873-1
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

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