Shear-free Null Quasi-Spherical Spacetimes

TL;DR

This paper investigates the residual gauge freedom in null quasi-spherical spacetimes, providing explicit formulas for key solutions, which aids in numerical relativity testing.

Contribution

It characterizes the gauge freedom in shear-free null foliations and derives explicit formulas for important spacetime solutions.

Findings

Explicit formulas for gauge transformations in Minkowski, Schwarzschild, Robinson-Trautman spacetimes

Identification of boost and rotation freedoms at each sphere

Application to numerical relativity test metrics

Abstract

The residual gauge freedom within the null quasi-spherical coordinate condition is studied, for spacetimes admitting an expanding, shear-free null foliation. The freedom consists of a boost and rotation at each coordinate sphere, corresponding to a specification of inertial frame at each sphere. Explicit formulae involving arbitrary functions of two variables are obtained for the accelerated Minkowski, Schwarzschild, and Robinson-Trautman spacetimes. These examples will be useful as test metrics in numerical relativity.