Universality of the thermodynamics of a quantum-mechanically radiating black hole departing from thermality

Mathur and Mehta won the third prize in the 2023 Gravity Research Foundation Essay Competition for proving the universality of black hole (BH) thermodynamics. Specifically, they demonstrated that any Extremely Compact Object (ECO) must have the same BH thermodynamic properties regardless of whether or not the ECO possesses an event horizon. The result is remarkable, but it was obtained under the approximation according to which the BH emission spectrum has an exactly thermal character. In fact, strong arguments based on energy conservation and BH back reaction imply that the spectrum of the Hawking radiation cannot be exactly thermal. In this work the result of Mathur and Mehta will be extended to the case where the radiation spectrum is not exactly thermal using the concept of BH dynamical state.
Comment: 13 pages,final version that matches the one published in Physics Letters B