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 a large class of solutions, including all black holes and neutral solutions. 
M. Azreg-Ainou, G. Clement, C.P. Constantinidis and J.C. Fabris