# Generalized G\"odel universes in higher dimensions and pure Lovelock gravity

## TL;DR

This paper generalizes G"odel universes to higher dimensions within Einstein and pure Lovelock gravity, introducing multiple rotations and constant curvature spaces for the first time.

## Contribution

It introduces a novel higher-dimensional G"odel universe model with multiple rotations and constant curvature spaces in Einstein and pure Lovelock gravity.

## Key findings

- Higher-dimensional G"odel universes constructed with multiple rotations.
- Inclusion of constant curvature spaces in the generalized models.
- First-time consideration of these generalizations in the literature.

## Abstract

G\"{o}del universe is a homogeneous rotating dust with negative $\Lambda$ which is a direct product of three dimensional pure rotation metric with a line. We would generalize it to higher dimensions for Einstein and pure Lovelock gravity with only one $N$th order term. For higher dimensional generalization, we have to include more rotations in the metric, and hence we shall begin with the corresponding pure rotation odd $(d=2n+1)$-dimensional metric involving $n$ rotations, which eventually can be extended by a direct product with a line or a space of constant curvature for yielding higher dimensional G\"{o}del universe. The considerations of $n$ rotations and also of constant curvature spaces is a new line of generalization and is being considered for the first time.