Electrostatic solutions in Kaluza-Klein theory: geometry and stability

We investigate the family of electrostatic spherically symmetric solutions of the five-dimensional Kaluza-Klein theory. Both charged and neutral cases are considered. The analysis of the solutions, through their geometrical properties, reveals the existence of black holes, wormholes and naked singularities. A new class of regular solutions is identified. A monopole perturbation study of all these solutions is carried out, enabling us to prove analytically the stability of large classes of solutions. In particular, the black hole solutions are stable, while for the regular solutions the stability analysis leads to an eigenvalue problem.Comment: Latex file, 21 page

Geometrical properties of Maslov indices in periodic-orbit theory

Maslov indices in periodic-orbit theory are investigated using phase space path integral. Based on the observation that the Maslov index is the multi-valued function of the monodromy matrix, we introduce a generalized monodromy matrix in the universal covering space of the symplectic group and show that this index is uniquely determined in this space. The stability of the orbit is shown to determine the parity of the index, and a formula for the index of the n-repetition of the orbit is derived.Comment: 18pages, 8figures, typos correcte