Electrovacuum Static Counter-Rotating Relativistic Dust Disks

TL;DR

This paper analyzes the counter-rotating model for electrostatic and magnetostatic thin disks in general relativity, deriving conditions for the velocities and densities of charged dust streams and exploring explicit solutions including Reissner-Nordstrom, Taub-NUT, and Kerr.

Contribution

It introduces a general constraint for counter-rotating velocities in charged dust disks and shows these streams follow electrogeodesics, providing explicit solutions in Einstein-Maxwell theory.

Findings

Derived a constraint for counter-rotating velocities.

Showed streams follow electrogeodesics with equal and opposite velocities.

Presented explicit solutions including Reissner-Nordstrom, Taub-NUT, and Kerr cases.

Abstract

A detailed study of the Counter-Rotating Model (CRM) for generic electrostatic (magnetostatic) axially symmetric thin disks without radial pressure is presented. We find a general constraint over the counter-rotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counter-rotating charged dust fluids. We then show that this constraint is satisfied if we take the two counter-rotating streams as circulating along electrogeodesics with equal and opposite tangential velocities. We also find explicit expressions for the energy densities, electrostatic (magnetostatic) charge densities and velocities of the counter-rotating fluids. Three specific examples are considered where we obtain some CRM well behaved based in simple solutions to the Einstein-Maxwell equations. The considered solutions are Reissner-Nordstrom in the electrostatic case, its magnetostatic counterpart and two solutions obtained from Taub-NUT and Kerr solutions.