Microscopic Models of Linear Dilaton Gravity and Their Semi-classical Approximations
We reanalyze and expand upon models proposed in 2015 for linear dilaton black holes, and use them to test several speculative ideas about black hole physics. We examine ideas based on the definition of quantum extremal surfaces in quantum field theory in curved space-time. The low energy effective field theory of our model is the large N CGHS model, which includes the one loop effects that are taken into account in the "island" proposal for understanding the Page curve. Contrary to the results of the island analysis, that solution leads to a singular geometry for the evaporated black hole. If the singularity obeys Cosmic Censorship then Hawking evaporation leaves behind a remnant object with a finite fraction of the black hole entropy. If the singularity becomes naked at some point, boundary conditions on a time-like line emanating from that point can produce a sensible model where we expect a Page curve. We show that the fully UV complete model gives a correct Page curve, as it must since the model is manifestly unitary. Recent result on replicawormholes suggest that the island formula, which appears to involve only one loop computations, in fact encodes non-perturbative contributions to the gravitational path integral. The question of why Euclidean gravity computations can capture information about microscopic states of quantum gravity remains mysterious. In a speculative coda to the paper we suggest that the proper way of understanding the relation between Euclidean gravity path integrals and quantum spectra is via a statistical approach to Jacobson's interpretation of general relativistic field equations as the hydrodynamic equations of the area law for the maximal entropy of causal diamonds.