In f(R) theories, the replica-method gravitational entropy computed on the apparent horizon matches the Hollands-Wald-Zhang dynamical black hole entropy and satisfies the first law, while the event horizon does not; this lets the generalized second law be reinterpreted as matter entanglement across
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The entropy of a dynamical black hole equals the area of its apparent horizon at second order in perturbations when the null energy condition holds.
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Entanglement Entropy and Thermodynamics of Dynamical Black Holes
In f(R) theories, the replica-method gravitational entropy computed on the apparent horizon matches the Hollands-Wald-Zhang dynamical black hole entropy and satisfies the first law, while the event horizon does not; this lets the generalized second law be reinterpreted as matter entanglement across
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The entropy of black hole under second-order deviation from equilibrium
The entropy of a dynamical black hole equals the area of its apparent horizon at second order in perturbations when the null energy condition holds.