Nonsingular Schwarzschild-de Sitter black holes in finite conformal quantum gravity

Abstract

In this work, we prove that the classical Schwarzschild-de Sitter spacetime is an exact solution of a class of weakly non-local, UV finite conformal quantum gravity theories, without the necessity of including a cosmological constant term in the action, thus associating the effective cosmological constant $\Lambda$ appearing in the metric with the coupling constants of the quantum gravity theory. Furthermore, exploiting the inherent conformal symmetry of the theory, we take advantage of the natural enlargement of the exact solutions to motivate the construction of a regular spacetime via conformal rescaling of the Schwarzschild-de Sitter spacetime. Moreover, we ensure the spacetime completeness by investigating the regularity of the curvature invariants and the geodesic completeness of conformally/non-conformally coupled massive and massless particles. We also study the global causal structure by explicitly constructing the Penrose diagram of the regular spacetime. Furthermore, as a result of the spacetime completeness analysis, we generalize the range of conformal factors that generate regular spacetimes, by considering the $N$ parameter of the conformal factor as a real parameter with a lower bound, and not only a positive integer, as constrained in previous studies on regular Schwarzschild/Kerr black holes. Thus, the present analysis broadens the range of solutions of the finite conformal quantum theory and opens the window to more precise observational tests of the theory using astrophysical data, by considering the accelerated expansion of the universe.