A family of relativistic charged thin disks with an inner edge

TL;DR

This paper introduces a new family of exact solutions to Einstein-Maxwell equations describing static, charged, axially symmetric thin disks with an inner edge, with well-behaved physical properties satisfying all energy conditions.

Contribution

It provides explicit metric functions for a novel family of static charged dust disks with an inner edge using the Ernst method, expanding the set of known solutions.

Findings

Energy density, pressure, and charge density are well-behaved everywhere.

Solutions satisfy all energy conditions.

Explicit metric functions are expressed in oblate spheroidal coordinates.

Abstract

A new family of exact solutions of the Einstein-Maxwell equations for static axially symmetric spacetimes is presented. The metric functions of the solutions are explicitely computed and are simply written in terms of the oblate spheroidal coordinates. The solutions, obtained by applying the Ernst method of complex potentials, describe an infinite family of static charged dust disks with an inner edge. The energy density, pressure and charge density of all the disks of the family are everywhere well behaved, in such a way that the energy-momentum tensor fully agrees with all the energy conditions.