G\"{o}del-type universes in unimodular gravity

TL;DR

This paper investigates G"{o}del-type universes within unimodular gravity to understand how causality violations manifest when the cosmological constant is an emergent integration constant.

Contribution

It explores the existence of G"{o}del solutions in unimodular gravity and analyzes their causal structure, highlighting conditions under which causality violations can occur.

Findings

Both causal and non-causal G"{o}del regions are possible depending on the source.

Unimodular gravity allows G"{o}del solutions without necessarily violating causality.

The role of the cosmological constant as an integration constant is crucial in these solutions.

Abstract

In this paper, the G\"{o}del-type universes are examined within the framework of unimodular gravity. Since the existence of G\"{o}del solutions is intrinsically related to the presence of a cosmological constant in general relativity, one can naturally wonder how the acausal structure of the G\"{o}del solutions behaves in different cosmological scenarios. One of the simplest, but important, frameworks within this context is the unimodular gravity, in which the cosmological constant emerges as an integration constant rather than a coupling constant. Hence, the validity of G\"{o}del-type solutions is scrutinized within the unimodular approach, examining whether this theory can address the known issue of causality violation in G\"{o}del universes. In detail, it is demonstrated that for certain gravitational sources, both causal and non-causal regions are permissible.