G\"{o}del and G\"{o}del-type universes in K-essence theory

TL;DR

This paper explores G"{o}del and G"{o}del-type solutions within k-essence gravity, analyzing conditions for their existence, causality violations, and the influence of different matter sources, revealing both causal and non-causal solutions.

Contribution

It determines the conditions under which G"{o}del-type solutions exist in k-essence theory for arbitrary functions and matter sources, highlighting the theory's capacity for causal and non-causal solutions.

Findings

Existence conditions for G"{o}del-type solutions in k-essence.

Both causal and non-causal solutions are possible.

Causality violations depend on matter sources and k-essence functions.

Abstract

In this paper, the G\"{o}del-type solutions within the k-essence theory are investigated. The consistency of field equations, causality violation and existence of closed timelike curves are studied. The conditions for existence of G\"{o}del and G\"{o}del-type solutions are determined for any function that defines the k-essence. By taking different sources of matter, it is shown that this theory of gravity allows causal and non-causal G\"{o}del-type solutions.