Charged particles in the Reissner-Nordstrom geometry

The multiyear problem of a two-body system consisting of a Reissner-Nordstr\"om black hole and a charged massive particle at rest is here solved by an exact perturbative solution of the full Einstein-Maxwell system of equations. The expressions of the metric and of the electromagnetic field, including the effects of the electromagnetically induced gravitational perturbation and of the gravitationally induced electromagnetic perturbation, are presented in closed analytic formulas. Particular attention is given to the analysis of the lines of force of the system formed by the black hole and the naked singularity describing the test particle. The new general relativistic effects leading to an electric Meissner effect are explored.