# Relativistic Static Thin Disks of Polarized Matter

## TL;DR

This paper presents a family of exact solutions for static, axially symmetric thin disks made of polarized matter within Einstein-Maxwell theory, providing explicit formulas for physical quantities and a specific example model.

## Contribution

It introduces a new family of exact solutions describing polarized thin disks in conformastatic spacetime, with explicit metric functions and electromagnetic potentials derived from Laplace equation solutions.

## Key findings

- Derived general expressions for energy density, pressure, and polarization.
- Presented the first specific model and analyzed physical variable behaviors.
- Provided explicit formulas for electromagnetic fields and velocities.

## Abstract

An infinite family of exact solutions of the electrovacuum Einstein-Maxwell equations is presented. The family is static, axially symmetric and describe thin disks composed by electrically polarized material in a conformastatic spacetime. The form of the conformastatic metric allows us to write down the metric functions and the electromagnetic potentials in terms of a solution of the Laplace equation. We find a general expression for the surface energy density of the disk, the pressure, the polarization vector, the electromagnetic fields and the velocity rotation for circular orbits. As an example, we present the first model of the family and show the behavior of the different physical variables.