Mass and entropy of asymptotically flat eternal quantum black holes in 2D

Abstract: Semi-classical dilaton gravity in (1+1)-dimensions remains one of the only arenas where quantum black holes can be exactly constructed, fully accounting for backreaction due to quantum matter. Here we provide a comprehensive analysis of the mass and thermodynamic properties of static asymptotically flat quantum black holes both analytically and numerically. First, we analytically investigate eternal quantum black hole solutions to a one-parameter family of analytically solvable models interpolating between Russo-Susskind-Thorlacius and Bose, Parker, and Peleg gravities. Examining these models in a semi-classically allowed parameter space, we find naked singularities may exist for quantum fields in the Boulware state. Using a quasi-local formalism, where we confine the black hole to a finite sized cavity, we derive the conserved energy and analyze the system's thermal behavior. Specifically, we show the semi-classical Wald entropy precisely equals the generalized entropy, accounting for both gravitational and fine grained matter entropies, and we find a range where the quantum black holes are thermally stable. Finally, we numerically construct eternal black hole solutions to semi-classical Callan-Giddings-Harvey-Strominger gravity and find their thermal behavior is qualitatively different from their analytic counterparts. In the process, we develop an analytic expansion of the solutions and find it accurately approximates the full numerical solutions in the semi-classical limit.