Effective refractive index tensor for weak field gravity
Abstract
Gravitational lensing in a weak but otherwise arbitrary gravitational field can be described in terms of a 3 x 3 tensor, the "effective refractive index". If the sources generating the gravitational field all have small internal fluxes, stresses, and pressures, then this tensor is automatically isotropic and the "effective refractive index" is simply a scalar that can be determined in terms of a classic result involving the Newtonian gravitational potential. In contrast if anisotropic stresses are ever important then the gravitational field acts similarly to an anisotropic crystal. We derive simple formulae for the refractive index tensor, and indicate some situations in which this will be important.
Keywords
Cite
@article{arxiv.gr-qc/0411034,
title = {Effective refractive index tensor for weak field gravity},
author = {Petarpa Boonserm and Celine Cattoen and Tristan Faber and Matt Visser and Silke Weinfurtner},
journal= {arXiv preprint arXiv:gr-qc/0411034},
year = {2007}
}
Comments
V1: 8 pages, no figures, uses iopart.cls. V2: 13 pages, no figures. Significant additions and clarifications. This version to appear in Classical and Quantum Gravity