Dynamical Charged N-body Equilibrium in Circular Dilaton Gravity

TL;DR

This paper develops exact solutions for equilibrium configurations of charged particles in circular (1+1) dilaton gravity, extending previous uncharged models and analyzing large particle number behavior.

Contribution

It provides the first exact equilibrium solutions for charged particles in circular dilaton gravity with N particles of equal mass and specific charge arrangements.

Findings

Exact solutions for two charged particles in circular dilaton gravity.

Extension of solutions to N particles with evenly spaced charges.

Analysis of large N behavior and relation to uncharged solutions.

Abstract

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 the circle with charges chosen so that the electric field satisfies $E^{2}=$constant. We discuss the relation of these solutions to the previous uncharged equilibrium solutions and examine the behavior when the number of particles is large. We comment on the challenges in further generalizing the solutions we obtain.