MG11 
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Abstract

Static pertubations of a Reissner-Nordstr\"om black hole by a charged massive particle

The interaction of a Reissner-Nordstr\"om black hole and a charged massive particle at rest is studied in the framework of perturbation theory. The solutions of the combined Einstein-Maxwell equations for both perturbed gravitational and electromagnetic fields at first order of the perturbation are exactly reconstructed by summing all multipoles, and are given explicit closed form expressions. In this linear approximation an horizon appears to form around the particle location, although its charge to mass ratio is greater than one: this result needs to be further explored and validated by by considering the full non linear problem, namely the corresponding exact two-body solution of the Einstein-Maxwell equations.

Static perturbations by a point mass on a Schwarzschild black hole

The static perturbations by a point mass on a Schwarzschild black hole background are studied in the framework of perturbation theory. It is shown that a solution free of singularities cannot exist using the standard approach by Regge and Wheeler. Adopting a different gauge allows to find the explicit form of the perturbation corresponding to a stable configuration, characterized by the presence of a \lq\lq strut'' between the particle and the black hole. The resulting perturbed metric with a conical singularity is shown to be the linearized form of the exact solution for two collinear uncharged black holes in static configuration belonging to the Weyl class.