Solar energy paper index
Black-hole evaporation from the semiclassical Einstein equations in 3+1 dimensions
One-line summary
A solar energy research paper on Black-hole evaporation from the semiclassical Einstein equations in 3+1 dimensions.
Engineering notes
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Chinese explanation / 中文解读
中文解读待补充：本站会优先为光伏效率、钙钛矿太阳能电池、储能技术、太阳能热利用、BIPV、并网技术等高价值论文补充中文说明。
Original 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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