Lagrangian evolution of the Weyl tensor

1 November 1994

journal article
Published by American Astronomical Society in The Astrophysical Journal

Vol. 435, 1-7
https://doi.org/10.1086/174787

Abstract

We derive the evolution equations for the electric and magnetic parts of the Weyl tensor for cold dust from both general relativity and Newtonian gravity. In a locally inertial frame at rest in the fluid frame, the Newtonian equations agree with those of general relativity. We give explicit expressions for the electric and magnetic parts of the Weyl tensor in the Newtonian limit. In general, the magnetic part does not vanish, implying that the Lagrangian evolution of the fluid is not purely local.

Keywords

COSMOLOGY
ELECTRIC FIELDS
GRAVITATION THEORY
LAGRANGIAN FUNCTION
MAGNETIC FIELDS
NEWTON THEORY
RELATIVITY
TENSORS
EQUATIONS OF MOTION
GRAVITATIONAL COLLAPSE
UNIVERSE

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Version 1, 1994-03-10, ArXiv

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