On Non-Commutative Correction of the G\"odel-type Metric

TL;DR

This paper investigates how non-commutative geometry alters the G"odel-type universe metric, affecting the critical radius for causality violation and potential time travel.

Contribution

It introduces non-commutative corrections to the G"odel-type metric, revealing modifications to the critical radius related to causality and time travel.

Findings

Non-commutativity modifies the critical radius for causality violation.

The non-commutative corrections influence the conditions for time travel.

The study provides a new perspective on non-commutative effects in cosmological models.

Abstract

In this paper, we will study non-commutative corrections in the metric tensor for the G\"{o}del-type universe, a model that has as its main characteristic the possibility of violation of causality, allowing therefore time travel. We also find that the critical radius in such a model, which eventually will determine the time travel possibility, is modified due to the non commutativity of spatial coordinates.