Nucleation of charged quantum de-Sitter$_{3}$ black holes

Abstract: We construct charged, static black holes in three-dimensional de Sitter (dS${3}$) space that exactly account for semi-classical backreaction effects due to quantum conformal matter. This is accomplished using braneworld holography, where an accelerating, electrically charged anti-de Sitter${4}$ black hole localizes on a Randall-Sundrum end-of-the-world brane. Absent of backreaction, the black hole disappears, leaving a chemical conical defect. The "quantum" black hole has a physical parameter space characterized by a shark-fin diagram, with extremal, Nariai, and ultracold limits. We give a detailed analysis of the horizon thermodynamics, where we find the heat capacity of charged and neutral dS$_{3}$ black holes features Schottky peaks. In particular, for a specific temperature range, charged quantum black holes behave as thermal systems with a finite number of energy levels available to their underlying microscopic degrees of freedom, beyond which many energy levels become available. Finally, we compute the probability of nucleating quantum dS black holes. Our work gives a first step to study quantum matter backreaction effects on dS black hole decay.