Quantum Black Holes: Perihelion Advance, Quasi Normal Modes and Classical/ Topological Thermodynamics

Abstract

We report on some properties of a quantum black hole obtained recently. The correction to the Newtonian gravitational potential is proportional to a coupling $\alpha$, which is the only free parameter of the theory. We constrain the coupling using the perihelion advance, we compute the quasi-normal modes for scalar (both massless and massive) and electromagnetic perturbations. We find that all modes computed here are complex numbers characterized by a positive real part and a negative imaginary part, while both parts increase with the mass of the test scalar field. Also thermodynamics properties are investigated from the classical and topological point of view. In this regard, the quantum black hole exhibits the same behavior as the classical Reissner-Nordstr\"om space-time, that is, it presents stable/unstable branches in the Gibbs potential, one generating point and a topological charge $W=0$.