V. Belinski

I.C.R.A.Net- International Center for Relativistic Astrophysics Network, University of Rome "La Sapienza"

Title: Equilibrium confgurations of two charged masses in General Relativity".

Author: G. Alekseev and V. Belinski

Abstract: A family of static asymptotically flat solutions for Einstein-Maxwell equations which describe two

non-rotating electrically charged massive objects (the Reissner - Nordstrom sources) in equilibrium is presented. From the exact expressions it is shown that mutual gravitational interaction of these sources can be balanced by their electrostatic interaction (without any struts) if the masses, charges and distance between them satisfy the balance equation. This equation shows that the equilibrium is not possible for two black holes or for two naked singularity objects. However, in the case when one of the sources is a black hole and another one is a naked singularityE the equilibrium is possibleE for some appropriate distance.E The derived equilibrium condition for large distances asymptotes the Newtonian condition. It is interesting that for sufficiently short distances even an uncharged Schwarzshild black hole can "hang" freely in the field of the Reissner-Nordstrom naked singularity center.

Donato Bini

Istituto per le Applicazioni del Calcolo ``M. Picone'', CNR I-00161 Rome, Italy , and ICRA, University of Rome, I-00185 Rome, Italy

Title talk: Frenet-Serret formalism for null world lines

Abstract: The Frenet-Serret curve analysis is extended from nonnull to null trajectories in a generic spacetime using the Newman-Penrose formalism, recovering old results which are not well known and clarifying the associated Fermi-Walker transport which has been left largely unexplored in the literature.This machinery is then used to discuss null circular orbits in stationary axisymmetric spacetimes using the Kerr spacetime as a concrete example, and to integrate the equations of parallel transport along null geodesics in any spacetime.