Uniqueness of Petrov type D spatially inhomogeneous irrotational silent models

Abstract

The consistency of the constraint with the evolution equations for spatially inhomogeneous and irrotational silent (SIIS) models of Petrov type I, demands that the former are preserved along the timelike congruence represented by the velocity of the dust fluid, leading to \emph{new} non-trivial constraints. This fact has been used to conjecture that the resulting models correspond to the spatially homogeneous (SH) models of Bianchi type I, at least for the case where the cosmological constant vanish. By exploiting the full set of the constraint equations as expressed in the 1+3 covariant formalism and using elements from the theory of the spacelike congruences, we provide a direct and simple proof of this conjecture for vacuum and dust fluid models, which shows that the Szekeres family of solutions represents the most general class of SIIS models. The suggested procedure also shows that, the uniqueness of the SIIS of the Petrov type D is not, in general, affected by the presence of a non-zero pressure fluid. Therefore, in order to allow a broader class of Petrov type I solutions apart from the SH models of Bianchi type I, one should consider more general ``silent'' configurations by relaxing the vanishing of the vorticity and the magnetic part of the Weyl tensor but maintaining their ``silence'' properties i.e. the vanishing of the curls of $E_{ab},H_{ab}$ and the pressure $p$.

arXiv commentLatex, 19 pages, no figures;(v2) some clarification remarks and an appendix are added; (v3) minor changes to match published version

References in corpus (30)

• General Relativistic Dynamics of Irrotational Dust: Cosmological Implications
• Self-Similarity in General Relativity \endtitle
• General Relativistic 1+3 Orthonormal Frame Approach Revisited
• The Covariant Approach to LRS Perfect Fluid Spacetime Geometries
• Linearisation instability of gravity waves?
• Integrability of irrotational silent cosmological models
• Dynamics of Silent Universes
• Gravitational Instability of Cold Matter
• Equations of Gravitational Instability are Non-Local
• A dynamical systems approach to the tilted Bianchi models of solvable type
• A Local View of the Observable Universe
• A Relativistic Approch to Gravitational Instability in the Expanding Universe: Second Order Lagrangian Solutions
• Dynamical systems approach to G2 cosmology
• Future Asymptotic Behaviour of Tilted Bianchi models of type IV and VIIh
• The Similarity Hypothesis in General Relativity
• The Future of Tilted Bianchi Universes
• Symmetries of Bianchi I space-times
• The Futures of Bianchi type VII0 cosmologies with vorticity
• Bianchi Cosmologies: A Tale of Two Tilted fluids
• Homothetic perfect fluid space-times
• Integrability Conditions for Irrotational Dust with a Purely Electric Weyl Tensor: A Tetrad Analysis
• Silent universes with a cosmological constant
• Self-similar Bianchi models: II. Class B models
• 3+1 description of silent universes: a uniqueness result for the Petrov type I vacuum case
• Self-similar Bianchi models: I. Class A models
• Irrotational dust with Div H=0
• Equilibrium points of the tilted perfect fluid Bianchi VI${}_h$ state space
• Petrov type I silent universes with G3 isometry group: the uniqueness result recovered
• On tilted perfect fluid Bianchi type VI${}_0$ self-similar models
• A geometric description of the intermediate behaviour for spatially homogeneous models

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• Intrinsic Conformal Symmetries in Szekeres models