Dynamical charged N-body equilibrium in circular dilaton gravity

We extend the problem of (1 + 1) circular dilaton gravity to include charged particles. We examine the two (charged)-particle case in detail and find an exact equilibrium solution. We then extend this to N-particles and obtain a solution for this case as well. This class of solutions corresponds to N-particles of the same mass, spaced evenly around a circle with charges chosen so that the electric field satisfies E2 = constant. We discuss how these solutions are related to the previous uncharged equilibrium solutions and examine the behaviour when the number of particles is large. We comment on the challenges in further generalizing the solutions we obtain.