On the degenerate phase boundaries

TL;DR

This paper investigates the nature of phase boundaries in Ashtekar's gravity, proposing criteria to distinguish null boundaries and clarifying the structure of degenerate and non-degenerate regions.

Contribution

It reformulates the phase boundary analysis using mapping language and establishes conditions under which the boundary is null.

Findings

The image of the boundary must be null.

Additional criteria are needed to determine nullness of the phase boundary.

Abstract

The structure of the phase boundary between degenerate and non-degenerate regions in Ashtekar's gravity has been studied by Bengtsson and Jacobson who conjectured that the "phase boundary" should always be null. In this paper, we reformulate the reparametrization procedure in the mapping language and distinguish a phase boundary from its image. It is shown that the image has to be null, while the nullness of the phase boundary requries more suitable criterion.