Regularity and Stability of Electrostatic Solutions in Kaluza-Klein Theory

We investigate the family of electrostatic spherically symmetric solutions of the five-dimensional Kaluza-Klein theory. Besides black holes and wormholes, a new class of geodesically complete solutions is identified. A monopole perturbation is carried out, enabling us to prove analytically the stability of large classes of solutions, including all black holes and neutral solutions.