Causal Anomalies in Kaluza-Klein Gravity Theories

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 Gödel type, whereas the induced matter Kaluza-Klein (IM-KK) gravity rules out noncausal Gödel-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 Gödel-type solutions of the STM-KK field equations are studied. It is shown that every Gödel-type perfect fluid solution is isometric to the unique dust solution of the STM-KK field equations. The question as to whether 5-D Gödel-type non-causal geometries induce any physically acceptable 4-D energy-momentum tensor is also addressed.

16 page. LaTex file. To appear in Int. J. Mod. Phys. A (1998)

References in corpus (3)

• Kaluza-Klein Gravity
• Rotating dust solutions of Einstein's equations with 3-dimensional symmetry groups, Part 3: All Killing fields linearly independent of u^α and w^α
• Riemannian Space-times of Gödel Type in Five Dimensions

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• Gödel-type Spacetimes in Induced Matter Gravity Theory
• Violation of causality in $f(T)$ gravity
• Homogeneous Gödel-type solutions in hybrid metric-Palatini gravity
• Superenergy and Supermomentum of Goedel Universes
• Energy-momentum and angular momentum of Goedel universes
• A Note on Segre Types of Second Order Symmetric Tensors in 5-D Brane-world Cosmology