Riemannian space-times of Gödel type in five dimensions

Rebouças, M. J.; Teixeira, A. F. F.

doi:10.1063/1.532281

Cited by 13 publications

(16 citation statements)

References 44 publications

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“…For the sake of completeness, we should mention that the equivalence problem techniques were used to investigate the five-dimensional Gödel-type and generalized Gödel-type pseudo-Riemannian spacetimes [46,47]. Furthermore, Gödel-type solutions with torsion were also investigated [48] through the equivalence problem techniques for Riemann-Cartan spacetimes [14,15,17].…”

Section: Three-dimensional Homogeneous Gödel-type Spacetimesmentioning

confidence: 99%

Equivalence of three-dimensional spacetimes

Sousa¹,

Fonseca²,

Romero³

2008

Class. Quantum Grav.

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A solution to the equivalence problem in three-dimensional gravity is given and a practically useful method to obtain a coordinate invariant description of local geometry is presented. The method is a nontrivial adaptation of Karlhede invariant classification of spacetimes of general relativity. The local geometry is completely determined by the curvature tensor and a finite number of its covariant derivatives in a frame where the components of the metric are constants. The results are presented in the framework of real two-component spinors in three-dimensional spacetimes, where the algebraic classifications of the Ricci and Cotton-York spinors are given and their isotropy groups and canonical forms are determined. As an application we discuss Gödel-type spacetimes in three-dimensional General Relativity. The conditions for local space and time homogeneity are derived and the equivalence of three-dimensional Gödel-type spacetimes is studied and the results are compared with previous works on four-dimensional Gödel-type spacetimes.

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Section: Three-dimensional Homogeneous Gödel-type Spacetimesmentioning

confidence: 99%

Equivalence of three-dimensional spacetimes

Sousa¹,

Fonseca²,

Romero³

2008

Class. Quantum Grav.

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“…The Gödel's solutions attract considerable interest because they describe rotating universes that possess the completely unexpected property of closed timelike curves (CTCs). However, generalized Gödel models which do not contain CTCs have been found in general relativity in the presence of massless scalar fields [5], and in gravity theories derived from an action containing terms quadratic in the Ricci curvature invariants [6], in five-dimensional gravity theories [7], or in string-inspired gravity theories [8]. We study both causal and non-causal Gödel universes and find their superenergetic properties.…”

Section: Introductionmentioning

confidence: 99%

Superenergy and supermomentum of Gödel universes

Dąbrowski¹,

Garecki²

2001

Class. Quantum Grav.

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We review the canonical superenergy tensor and the canonical angular supermomentum tensors in general relativity and calculate them for space-time homogeneous Gödel universes to show that both of these tensors do not, in general, vanish. We consider both an original dust-filled pressureless acausal Gödel model of 1949 and a scalar-field-filled causal Gödel model of Rebouças and Tiomno. For the acausal model, the non-vanishing components of superenergy of matter are different from those of gravitation. The angular supermomentum tensors of matter and gravitation do not vanish either which simply reflects the fact that Gödel universe rotates. However, the axial (totally antisymmetric) and vectorial parts of supermomentum tensors vanish. It is interesting that superenergetic quantities are sensitive to causality in a way that superenergy density g S 00 of gravitation in the acausal model is positive, while superenergy density g S 00 in the causal model is negative. That means superenergetic quantities might serve as criterion of causality in cosmology and prove useful. PACS number(s): 98.80.Hw

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“…(2.14) hold for all the above solutions of the STM-KK theory. But for arbitrary constants m 2 and ω, equations (2.10) and (2.14) are the necessary and sufficient conditions for a 5-D Gödel-type manifold to be (locally) homogeneous [76]. Therefore, taking also into account the theorem 2 of Ref.…”

Section: Respectivelymentioning

confidence: 99%

Causal Anomalies in Kaluza–klein Gravity Theories

Rebouças

Teixeira

1998

Int. J. Mod. Phys. A

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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.Kaluza-Klein-type theories in five or more dimensions have been of interest in a few contexts. In the framework of gauge theories they have been used in the quest for unification of the fundamental interactions in physics. The idea that the various interactions in nature might be unified by enlarging the dimensionality of the space-time has a long history that goes back to the works of Kaluza and Klein [1] - [2]. They showed how one could unify Einstein's theory of gravitation and Maxwell's theory of electromagnetism in a five-dimensional framework. The higher-dimensional Kaluza-Klein approach to unification was later used by the unified-field theorists, especially among those investigating the eleven-dimensional supergravity and ten-dimensional superstrings.In 1983, Wesson [3,4] has given an impetus to the study of Kaluza-Klein type theories by investigating a five-dimensional Kaluza-Klein theory of gravitation with a variable rest mass. In this theory we have five-dimensional (5-D) space-time-mass manifolds, and the fifth dimension is a convenient mathematical way of geometrizing the rest mass and of allowing one to study the possibility that it may be variable. The four-dimensional (4-D) general relativity theory is recovered when the rate of change of the rest mass is zero.We shall refer to this theory as space-time-mass Kaluza-Klein gravity theory (STM-KK gravity theory, for short). Ever since the foundations of the STM-KK gravity theory were laid, there have been investigations on its potentialities, particularly as concerns to its consequences for astrophysics and cosmology, the confrontation between theory and observation, its consistency with Mach's principle, the solutions to its field equations, and the like [4] - [18]. For fair list of references on the STM-KK theory see Overduin andWesson [19].More recently, Wesson and co-workers [5,20] have introduced a new approach to general relativity, conceptually in line with an old idea due to Einstein [21], in which the matter and its role in the determination of the space-time geometry is given from a purely f...

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Riemannian space-times of Gödel type in five dimensions

Cited by 13 publications

References 44 publications

Equivalence of three-dimensional spacetimes

Equivalence of three-dimensional spacetimes

Superenergy and supermomentum of Gödel universes

Causal Anomalies in Kaluza–klein Gravity Theories

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