An analytic semiclassical model produces closed-form first-order corrections to the Hawking temperature and horizon position for a Schwarzschild black hole in a finite cavity.
(8) Equation ( 7) follows directly from the tt component of the Einstein tensor and generalizes the Misner–Sharp mass relation to the semiclassical regime
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Analytic semiclassical backreaction of a Schwarzschild black hole in a finite cavity: horizon shift, temperature renormalization, and canonical stability in the Hartle-Hawking State
An analytic semiclassical model produces closed-form first-order corrections to the Hawking temperature and horizon position for a Schwarzschild black hole in a finite cavity.