Causal Anomalies in Kaluza-Klein Gravity Theories

TL;DR

This paper investigates causality violations in Kaluza-Klein gravity theories, finding that induced matter models prevent G"odel-type noncausal solutions, thus offering a way to address causal anomalies in higher-dimensional gravity theories.

Contribution

It demonstrates that induced matter Kaluza-Klein gravity excludes noncausal G"odel-type solutions, unlike the space-time-mass model, providing a new approach to resolving causal anomalies.

Findings

Induced matter Kaluza-Klein gravity rules out G"odel-type causality violations.

Space-time-mass Kaluza-Klein gravity allows G"odel-type causal violations.

Every G"odel-type perfect fluid solution is isometric to a dust solution in STM-KK theory.

Abstract

Causal anomalies in two Kaluza-Klein gravity theories are examined, particularly as to whether these theories permit solutions in which the causality principle is violated. It is found that similarly to general relativity the field equations of the space-time-mass Kaluza-Klein (STM-KK) gravity theory do not exclude violation of causality of G\"odel type, whereas the induced matter Kaluza-Klein (IM-KK) gravity rules out noncausal G\"odel-type models. The induced matter version of general relativity is shown to be an efficient therapy for causal anomalies that occurs in a wide class of noncausal geometries. Perfect fluid and dust G\"odel-type solutions of the STM-KK field equations are studied. It is shown that every G\"odel-type perfect fluid solution is isometric to the unique dust solution of the STM-KK field equations. The question as to whether 5-D G\"odel-type non-causal geometries induce any physically acceptable 4-D energy-momentum tensor is also addressed.