Black holes and covariance in effective quantum gravity: A solution without Cauchy horizons

Abstract: As a continuation of our previous work addressing general covariance in effective quantum gravity models within the Hamiltonian framework, this study presents explicit derivations of the previously proposed covariance equation. By solving this equation, a new Hamiltonian constraint is obtained, incorporating free functions that can account for quantum gravity effects. Specifying these functions allows for an analysis of the resulting spacetime structure. Remarkably, in this model, the classical singularity is replaced by a region where the metric asymptotically approaches a Schwarzschild-de Sitter one with negative mass. Unlike previously studied spacetime structures, this new quantum-corrected model avoids the presence of Cauchy horizons, potentially suggesting its stability under perturbations. Finally, the covariance of dust field coupling within the effective model is examined.