Finite axisymmetric charged dust disks in conformastatic spacetimes

TL;DR

This paper constructs finite, axisymmetric charged dust disks in conformastatic spacetimes by solving Einstein-Maxwell equations, using generalized Kalnajs disks, resulting in well-behaved, physically consistent galaxy models with balanced electromagnetic and gravitational forces.

Contribution

It introduces a new family of exact solutions for charged dust disks based on generalized Kalnajs disks within conformastatic spacetimes, linking electromagnetic and gravitational equilibrium.

Findings

Disks have positive, well-behaved energy density vanishing at edges.

Electric charge density closely matches mass density, ensuring force balance.

Solutions satisfy all energy conditions and represent realistic galaxy models.

Abstract

An infinite family of axisymmetric charged dust disks of finite extension is presented. The disks are obtained by solving the vacuum Einstein-Maxwell equations for conformastatic spacetimes, which are characterized by only one metric function. In order to obtain the solutions, it is assumed that the metric function and the electric potential are functionally related and that the metric function is functionally dependent of another auxiliary function, which is taken as a solution of Laplace equation. The solutions for the auxiliary function are then taken as given by the infinite family of generalized Kalnajs disks recently obtained by Gonz\'alez and Reina (MNRAS 371, 1873, 2006), which is expressed in terms of the oblate spheroidal coordinates and represents a well behaved family of finite axisymmetric flat galaxy models. The so obtained relativistic thin disks have then a charge density that is equal, except maybe by a sign, to their mass density, in such a way that the electric and gravitational forces are in exact balance. The energy density of the disks is everywhere positive and well behaved, vanishing at the edge. Accordingly, as the disks are made of dust, their energy-momentum tensor it agrees with all the energy conditions.