Lagrangian Evolution of the Weyl Tensor
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.
 Publication:

The Astrophysical Journal
 Pub Date:
 November 1994
 DOI:
 10.1086/174787
 arXiv:
 arXiv:astroph/9403016
 Bibcode:
 1994ApJ...435....1B
 Keywords:

 Cosmology;
 Electric Fields;
 Gravitation Theory;
 Lagrangian Function;
 Magnetic Fields;
 Newton Theory;
 Relativity;
 Tensors;
 Equations Of Motion;
 Gravitational Collapse;
 Universe;
 Astrophysics;
 COSMOLOGY: THEORY;
 GRAVITATION;
 COSMOLOGY: LARGESCALE STRUCTURE OF UNIVERSE;
 Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 17 pages, AAS LateX v3.0, submitted to ApJ, MITCSR9406