Rotating and counterrotating relativistic thin disks as sources of stationary electrovacuum spacetimes

TL;DR

This paper analyzes the counterrotating model for stationary axially symmetric relativistic thin disks in electrovacuum, exploring conditions for their construction, and presents models based on Kerr-Newman solutions that satisfy energy conditions.

Contribution

It provides a general constraint for counterrotating velocities in charged thin disks and develops models using Kerr-Newman solutions with well-behaved counterrotating disks.

Findings

Counterrotating velocities can sometimes be equal and opposite or follow electro-geodesics.

Disks constructed from Kerr-Newman solutions satisfy all energy conditions.

Models exhibit purely azimuthal pressure without heat flow.

Abstract

A detailed study is presented of the counterrotating model (CRM) for electrovacuum stationary axially symmetric relativistic thin disks of infinite extension without radial stress, in the case when the eigenvalues of the energy-momentum tensor of the disk are real quantities, so that there is not heat flow. 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 then show that, in some cases, this constraint can be satisfied if we take the two counterrotating tangential velocities as equal and opposite or by taking 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. A simple family of models of counterrotating charged disks based on the Kerr-Newman solution are considered where we obtain some disks with a CRM well behaved. We also show that the disks constructed from the Kerr-Newman solution can be interpreted, for all the values of parameters, as a matter distribution with currents and purely azimuthal pressure without heat flow. The models are constructed using the well-known "displace, cut and reflect" method extended to solutions of vacuum Einstein-Maxwell equations. We obtain, in all the cases, counterrotating Kerr-Newman disks that are in agreement with all the energy conditions.