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arXiv · 2607.11737

Black-hole evaporation from the semiclassical Einstein equations in 3+1 dimensions

Adrián del Río·F. Javier Marañón-González
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Abstract

We solve the semiclassical Einstein equations for an evaporating Schwarzschild black hole in closed form, obtaining its backreacted geometry in 3+1 dimensions. This is achieved by a reformulation of the Hadamard renormalization prescription, which admits explicit stress-energy tensors for scalar quantum fields in 3+1-dimensional curved spacetimes without the standard mode-sum construction. The Unruh-like states we construct reproduce the Hawking flux at future null infinity and the associated ingoing negative-energy flux at the horizon, yielding the first analytical quasi-stationary solution describing black-hole evaporation in four-dimensional semiclassical gravity. The resulting geometry exhibits a timelike apparent horizon, providing a new analytical setting to study the causal structure of black-hole evaporation and its connection with the information-loss issue. Our results open a new route to semiclassical backreaction in four dimensions, extending the level of analytical control previously available only in two-dimensional effective models.

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Adrián del Río, F. Javier Marañón-González. 2026-07-13. Black-hole evaporation from the semiclassical Einstein equations in 3+1 dimensions. https://arxiv.org/abs/2607.11737

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