Generalized Robertson-Walker space times, a survey

Abstract

Generalized Robertson-Walker spacetimes extend the notion of Robertson-Walker spacetimes, by allowing for spatial non-homogeneity. A survey is presented, with main focus on Chen's characterization in terms of a timelike concircular vector. Together with their most important properties, some new results are presented.

arXiv comment23 pages. Accepted for publication on Int. J. Geom. Meth. Mod. Phys

References in corpus (19)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state
• Phantom Energy and Cosmic Doomsday
• A simple characterization of generalized Robertson-Walker spacetimes
• Cosmology with a stiff matter era
• Causal Thermodynamics in Relativity
• A condition for a perfect-fluid space-time to be a generalized Robertson-Walker space-time
• Uniqueness of spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker spacetimes
• Weakly Z symmetric manifolds
• On the Weyl and Ricci tensors of Generalized Robertson-Walker space-times
• Global decomposition of a Lorentzian manifold as a Generalized Robertson-Walker space
• Minimal tensors and purely electric or magnetic spacetimes of arbitrary dimension
• Killing and Conformal Killing tensors
• Weyl compatible tensors
• Yang's gravitational theory
• Relativistic self-gravitating Bose-Einstein condensates and cold baryons with a stiff equation of state
• Killing Tensors and Conformal Killing Tensors from Conformal Killing Vectors
• Spacelike hypersurfaces of constant higher order mean curvature in generalized Robertson-Walker spacetimes
• A note on extended Lorentzian recurrent manifolds

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