On the Newtonian Limit of the Weyl Tensor

Abstract

In this note we wish to complement some recent work in the cosmological literature concerning the Weyl conformal curvature tensor and its parts. In particular, we shall give a clear-cut definition of the Newtonian limits of electric and magnetic parts of the Weyl tensor. We also discuss that only a subset of the relativistic equations is needed to obtain a closed system of equations in the Newtonian limit.

arXiv comment6 pages. Dedicated to the memory of Juergen Ehlers. To appear in the upcoming Special Issue of "General Relativity and Gravitation"

References in corpus (13)

• Dark Energy from structure: a status report
• General Relativistic 1+3 Orthonormal Frame Approach Revisited
• Newtonian Cosmology in Lagrangian Formulation: Foundations and Perturbation Theory
• Integrability of irrotational silent cosmological models
• Dynamics of Silent Universes
• Post-Newtonian Cosmological Dynamics in Lagrangian coordinates
• Lagrangian Evolution of the Weyl Tensor
• The Cosmic No-Hair Theorem and the Nonlinear Stability of Homogeneous Newtonian Cosmological Models
• Gravitational Instability of Cold Matter
• Equations of Gravitational Instability are Non-Local
• A Relativistic Approch to Gravitational Instability in the Expanding Universe: Second Order Lagrangian Solutions
• Newtonian Evolution of the Weyl Tensor
• Irrotational dust with Div H=0

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