The authors derive non-perturbative first and second laws for dynamical black holes, identifying entropy with the area of local marginally trapped surfaces rather than the global event horizon.
Varadarajan, Spherical collapse and black hole evaporation, Phys
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Thermodynamics of dynamical black holes beyond perturbation theory
The authors derive non-perturbative first and second laws for dynamical black holes, identifying entropy with the area of local marginally trapped surfaces rather than the global event horizon.