Effective refractive index tensor for weak field gravity

Details Effective refractive index tensor for weak field gravity Effective refractive index tensor for weak field gravity

2004-11-08

arxiv.org/abs/gr-qc/0411034v2

Class.Quant.Grav. 22 (2005) 1905-1916

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

V1: 8 pages, no figures, uses iopart.cls. V2: 13 pages, no figures. Significant additions and clarifications. This version to

Scientific paper

10.1088/0264-9381/22/11/001

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.

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