Action integrals for quantum BTZ black holes

Black holes exactly incorporating quantum matter backreaction effects, namely, quantum black holes, are notoriously difficult to construct, let alone study their horizon thermodynamics. Here, we derive the thermodynamics of three-dimensional charged and rotating quantum black holes via the tree-level gravitational partition function. Specifically, we primarily focus on holographic quantum BTZ black holes, dual to $(3+1)$-dimensional accelerating black holes in anti-de Sitter space that localize on Karch-Randall end-of-the-world (ETW) branes. To derive their horizon thermodynamics, we regulate the bulk Euclidean geometry by adding a second ETW brane at asymptotic spatial infinity. We compute the on-shell action of the complexified accelerating black hole in the grand canonical ensemble and derive the quantum BTZ black hole thermodynamics, where the thermal entropy is equal to the generalized entropy. This provides a first principles derivation of the generalized entropy of three-dimensional quantum black holes. Further, we construct charged and rotating quantum black holes in three-dimensional de Sitter and Minkowski space using Randall-Sundrum ETW branes, and compute their horizon thermodynamics.