Mass inflation and strong cosmic censorship conjecture in the covariant quantum black hole

Abstract

Recently, two types of solutions to the long-standing issue of general covariance in canonical quantum gravity have been proposed. From the above, a fundamental question arises: which solution is superior? Considering one type of solution with a Cauchy horizon, in the present letter, we explore whether it exhibits properties similar to those of the Reissner-Nordstr\"{o}m black hole. Due to its geometric similarity, application of the generalized Dray-'t Hooft-Redmond relation reveals evidence of mass inflation, indicating that the Cauchy horizon is unstable. While this is consistent with the Strong Cosmic Censorship conjecture, it suggests that it does not represent a regular black hole. Furthermore, we extend the metric to include a cosmological constant and study the validity of the Strong Cosmic Censorship conjecture for the quantum black hole in de Sitter spacetime. After taking into account the reasonable ranges of parameters for the quantum black hole, we find that the Strong Cosmic Censorship Conjecture holds.