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Entanglement entropy of near-extremal black hole

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arxiv 2202.10259 v1 pith:R26TG3TK submitted 2022-02-21 hep-th

Entanglement entropy of near-extremal black hole

classification hep-th
keywords entropyblackentanglementholemasschargeconstraintdecreasing
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We study how the entanglement entropy of the Hawking radiation derived using island recipe for the Reissner-Nordstr\"om black hole behaves as the black hole mass decreases. A general answer to the question essentially depends not only on the character of decreasing of the mass but also on decreasing of the charge. We assume the specific relationship between the charge and mass $Q^2=GM^2[1-\left(\frac{M}{\mu}\right)^{2\nu} ]$, which we call the constraint equation. We discuss whether it is possible to have a constraint so that the entanglement entropy does not have an explosion at the end of evaporation, as happens in the case of thermodynamic entropy and the entanglement entropy for the Schwarzschild black hole. We show that for some special scaling parameters, the entanglement entropy of radiation does not explode as long as the mass of the evaporating black hole exceeds the Planck mass.

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    Fuzzball models with stretched horizons modify or eliminate entanglement islands depending on boundary conditions and cap geometry, producing information paradox analogues in some cases.