Universality of black hole thermodynamics beyond the thermal approximation

Mathur and Mehta were awarded the third prize in the 2023 Gravity Research Foundation Essay Competition for their work demonstrating the universality of black hole (BH) thermodynamics. Their research established that any Extremely Compact Object (ECO) exhibits the same thermodynamic properties as a BH, irrespective of the presence of an event horizon. This significant finding was derived under the assumption that the BH emission spectrum behaves thermally. However, compelling arguments rooted in energy conservation and the BH back reaction indicate that the spectrum of Hawking radiation cannot be perfectly thermal. In this paper, we explore the extension of Mathur and Mehta’s findings to scenarios where the radiation spectrum deviates from exact thermal behavior, utilizing the concept of the BH dynamical state.