# Rotating AdS Einstein universes from constrained metrics

## TL;DR

This paper demonstrates that imposing constraints on the metric tensor in rotating AdS spacetimes simplifies the equations of motion, leading to new solution families with some freely specifiable functions.

## Contribution

It introduces a method to reduce the equations of motion in rotating AdS spaces via metric constraints, revealing new solution families with undetermined functions.

## Key findings

- Derived new analytic solutions for constrained rotating AdS geometries.
- Reduced the number of independent equations in rotating AdS spacetimes.
- Found solutions applicable to both vacuum and matter-containing black holes.

## Abstract

The imposition of a constraint between the metric tensor elements in both three- and four-dimensional, rotating AdS space-times is shown to reduce the number of independent equations of motion and to result in new families of solutions to the equations of motion. For the geometries investigated analytic solutions or partial analytic solutions of the equations of motion are obtained. In all cases the number of independent field equations is less than the number of independent functions, resulting in an undetermined function which can be freely specified. For rotating, asymptotically $AdS$ space-times the reduction of the number of field equations to be solved holds for vacuum black hole solutions and for black hole solutions obtained from space-times containing matter.