Shear free solutions in General Relativity Theory

Details Shear free solutions in General Relativity Theory Shear free solutions in General Relativity Theory

2011-07-19

arxiv.org/abs/1107.3669v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, no figures. For GRG special issue in honor of Josh Goldberg

Scientific paper

The Goldberg-Sachs theorem is an exact result on shear-free null geodesics in a vacuum spacetime. It is compared and contrasted with an exact result for pressure-free matter: shear-free flows cannot both expand and rotate. In both cases, the shear-free condition restricts the way distant matter can influence the local gravitational field. This leads to intriguing discontinuities in the relation of the General Relativity solutions to Newtonian solutions in the timelike case, and of the full theory to the linearised theory in the null case. It is a pleasure to dedicate this paper to Josh Goldberg.

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