# Three-dimensional axisymmetric sources for Majumdar-Papapetrou type spacetimes

## TL;DR

This paper constructs three-dimensional axisymmetric relativistic sources based on Newtonian potential-density pairs for Majumdar-Papapetrou spacetimes, modeling galaxy structures and analyzing particle motion and stability.

## Contribution

It introduces a method to generate relativistic galaxy models from Newtonian potentials, including thick disks and multi-component systems, satisfying energy conditions.

## Key findings

- Relativistic effects are significant compared to Newtonian models.
- Models satisfy all energy conditions.
- Orbital stability is analyzed using an extended Rayleigh criterion.

## Abstract

From Newtonian potential-density pairs we construct three-dimensional axisymmetric relativistic sources for a Majumdar-Papapetrou type conformastatic spacetime. As simple examples, we build two family of relativistic thick disks from of the first two Miyamoto-Nagai potential-density pairs used in Newtonian gravity to model flat galaxies, and a three-component relativistic model of galaxy (bulge, disk and dark matter halo). We study the equatorial circular motion of test particles around such structures. Also the stability of the orbits is analyzed for radial perturbation using an extension of the Rayleigh criterion. In all examples, the relativistic effects are analyzed and compared with the Newtonian approximation. The models considered satisfying all the energy conditions.