The Constraints in Spherically Symmetric General Relativity III --- Identifying the Configuration Space: $J\ne 0$

TL;DR

This paper extends the analysis of constraints in spherically symmetric general relativity to configurations with non-zero angular momentum, providing foliation-independent characterizations of horizons and singularities.

Contribution

It generalizes previous work to include non-zero angular momentum and demonstrates foliation-independent methods for identifying horizons and singularities.

Findings

Characterization of apparent horizons and singularities independent of foliation

Extension of the analysis to configurations with J ≠ 0

Use of foliations linear and homogeneous in extrinsic curvature

Abstract

We continue our examination of the constraints in spherically symmetric general relativity begun in I (gr-qc/9411009) and II (gr-qc/9411010). We extend to general configurations with $J\ne 0$ the analysis of II which treated a moment of time symmetry. We exploit the one parameter family of foliations introduced in I which are linear and homogeneous in the extrinsic curvature to characterize apparent horizons and spatial singularities in the initial data. In particular, we demonstrate that these characterizations do not depend sensitively on the foliation.