Finite Axisymmetric Charged Dust Disks Sources for Conformastatic Spacetimes

TL;DR

This paper constructs finite, axisymmetric charged dust disk models in conformastatic spacetimes by solving Einstein-Maxwell equations with a specific electromagnetic-metric potential relation, providing exact solutions and examples.

Contribution

It introduces a method to generate finite charged dust disk solutions in conformastatic spacetimes using an inverse approach based on Laplace equation solutions.

Findings

Derived exact conformastatic metrics with finite charged dust disks.

Established proportionality between charge density and energy surface density.

Provided explicit examples of disk solutions with finite extension.

Abstract

An infinite family of finite axisymmetric charged dust disks is presented. The disks are obtained by solving the Einstein-Maxwell equations for conformastatic spacetimes by assuming a functional dependency between the time-like component of the electromagnetic potential and the metric potential in terms of a solution of the Laplace equation. We give solutions to the Einstein-Maxwell equations with disk sources of finite extension in which the charge density is proportional to the energy surface density. We apply the well-know "inverse" approach to the gravitational potential representing finite thin disks given by Gonzalez and Reina to generate conformastatic charged dust thin discs. Exact examples of conformastatic metrics with disk sources are worked out in full.