Exact Relativistic Static Charged Perfect Fluid Disks

TL;DR

This paper constructs static charged perfect fluid disks from Einstein's equations using a specific method, analyzes their stability, and finds that charge tends to increase instability regions.

Contribution

It introduces a new approach to generate charged perfect fluid disks and derives a simple stability criterion considering charge effects.

Findings

Charge increases the instability regions of the disks.

Disks are constructed from the Reissner-Nordström solution in isotropic coordinates.

A stability condition for charged and uncharged disks is derived.

Abstract

Using the well-known ``displace, cut and reflect'' method used to generate disks from given solutions of Einstein field equations, we construct static charged disks made of perfect fluid based on the Reissner-Nordstr\"{o}m solution in isotropic coordinates. We also derive a simple stability condition for charged and non charged perfect fluid disks. As expected, we find that the presence of charge increases the regions of instability of the disks.