Electrovacuum Static Counterrotating Relativistic Dust Disks

TL;DR

This paper analyzes the counterrotating model for static electrovacuum thin disks, deriving conditions for charged dust fluids to replicate the disk's energy-momentum tensor, and explores specific models based on known solutions.

Contribution

It provides a general constraint on counterrotating velocities and explicit expressions for physical quantities, extending the CRM to electrovacuum thin disks with new model families.

Findings

Counterrotating velocities can be aligned along electro-geodesics under certain conditions.

Explicit formulas for energy and charge densities of counterrotating fluids are derived.

Several models based on classical solutions are constructed with well-behaved CRM properties.

Abstract

A detailed study is presented of the counterrotating model (CRM) for generic electrovacuum static axially symmetric relativistic thin disks without radial pressure. We find a general constraint over the counterrotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counterrotating charged dust fluids. We also find explicit expressions for the energy densities, charge densities and velocities of the counterrotating fluids. We then show that this constraint can be satisfied if we take the two counterrotating streams as circulating along electro-geodesics. However, we show that, in general, it is not possible to take the two counterrotating fluids as circulating along electro-geodesics nor take the two counterrotating tangential velocities as equal and opposite. Four simple families of models of counterrotating charged disks based on Chazy-Curzon-like, Zipoy-Voorhees-like, Bonnor-Sackfield-like and Kerr-like electrovacuum solutions are considered where we obtain some disks with a CRM well behaved. The models are constructed using the well-known ``displace, cut and reflect'' method extended to solutions of vacuum Einstein-Maxwell equations.