Matter collineations of Spacetime Homogeneous Gödel-type Metrics

Abstract

The spacetime homogeneous Gödel-type spacetimes which have four classes of metrics are studied according to their matter collineations. The obtained results are compared with Killing vectors and Ricci collineations. It is found that these spacetimes have infinite number of matter collineations in degenerate case, i.e. det$(T_{ab})=0$, and do not admit proper matter collineations in non-degenerate case, i.e. det$(T_{ab})\ne 0$. The degenerate case has the new constraints on the parameters $m$ and $w$ which characterize the causality features of the Gödel-type spacetimes.

arXiv comment12 pages, LaTex, no figures, Class. Quantum.Grav.20 (2003) 2169

References in corpus (6)

• Ricci Collineations of the Bianchi Types I and III, and Kantowski-Sachs Spacetimes
• Gödel-type Spacetimes in Induced Matter Gravity Theory
• Computation of the conformal algebra of 1+3 decomposable spacetimes
• Ricci Collineations of the Bianchi Type II, VIII, and IX Space-times
• Ricci Collineations for type B warped space-times
• Classification of Spherically Symmetric Static Spacetimes according to their Matter Collineations

Cited by in corpus (15)

• Gödel-type universes in f(R) gravity
• Symmetries of geodesic motion in Gödel-type spacetimes
• Gödel-type universes and chronology protection in Horava-Lifshitz gravity
• Classification of Static Plane Symmetric Spacetimes according to their Matter Collineations
• Symmetries of the Energy-Momentum Tensor of Cylindrically Symmetric Static Spacetimes
• Symmetries of the Energy-Momentum Tensor of Spherically Symmetric Lorentzian Manifolds
• Conformal symmetries of the energy-momentum tensor of spherically symmetric static spacetimes
• Symmetries of Locally Rotationally Symmetric Models
• On the definition of matter collineations
• Symmetries of the Energy-Momentum Tensor: Some Basic Facts
• Matter Inheritance Symmetries of Spherically Symmetric Static Spacetimes
• Symmetries of Lorentzian Three-Manifolds with Recurrent Curvature
• Addendum: Symmetries of the energy-momentum tensor
• On symmetries of the Heisenberg group
• Noether symmetries of the minimal surface Lagrangian for Gödel-type spacetimes