The apparent horizon shape is derived to second order for perturbed evaporating black holes, and an effective classical metric is obtained from quantum expectation values of the reconstructed spacetime.
Quantum Field Theory of Black Hole Perturbations with Backreaction V. Beyond Second Order Perturbations,
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Quantum Field Theory of Black Hole Perturbations with Backreaction VI. Apparent Horizons, Quasi-Local Mass and Effective Classical Metrics
The apparent horizon shape is derived to second order for perturbed evaporating black holes, and an effective classical metric is obtained from quantum expectation values of the reconstructed spacetime.