Lagrangian Evolution of the Weyl Tensor
Astrophysics
2009-10-22 v1 General Relativity and Quantum Cosmology
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.
Cite
@article{arxiv.astro-ph/9403016,
title = {Lagrangian Evolution of the Weyl Tensor},
author = {Edmund Bertschinger and A. J. S. Hamilton},
journal= {arXiv preprint arXiv:astro-ph/9403016},
year = {2009}
}
Comments
17 pages, AAS LateX v3.0, submitted to ApJ, MIT-CSR-94-06