On causality violation in Lyra Geometry

TL;DR

This paper investigates causality issues in Lyra geometry, a non-Riemannian framework derived from Weyl geometry, analyzing solutions like G"odel metrics and their implications for causality without matter sources.

Contribution

It explores causality violations in Lyra geometry and presents novel solutions for G"odel universes without matter, comparing them with general relativity.

Findings

G"odel and G"odel-type metrics are compatible with Lyra geometry.

A matter-free G"odel universe solution is found in Lyra geometry.

Conditions for causal and non-causal solutions are discussed.

Abstract

In this paper the causality issues are discussed in a non-Riemannian geometry, called Lyra geometry. It is a non-Riemannian geometry originated from Weyl geometry. In order to compare this geometry with the Riemannian geometry, the Einstein field equations are considered. It is verified that the G\"{o}del and G\"{o}del-type metric are consistent with this non-Riemannian geometry. A non-trivial solution for G\"{o}del universe in the absence of matter sources is determined without analogue in general relativity. Different sources are considered and then different conditions for causal and non-causal solutions are discussed.