Shear free solutions in General Relativity Theory

TL;DR

This paper explores shear-free null geodesics and matter flows in General Relativity, highlighting how shear-free conditions influence gravitational fields and reveal differences from Newtonian and linearized theories.

Contribution

It compares shear-free solutions in vacuum and matter contexts, revealing how shear-free conditions constrain gravitational influences and cause discontinuities with Newtonian and linearized solutions.

Findings

Shear-free null geodesics are characterized by the Goldberg-Sachs theorem.

Shear-free pressure-free matter flows cannot both expand and rotate.

Discontinuities arise between GR solutions and Newtonian or linearized theories.

Abstract

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.