Causal structure and degenerate phase boundaries

TL;DR

This paper investigates the causal structure of degenerate space-times in Ashtekar gravity, proving that phase boundaries separating degenerate and non-degenerate regions are null under specific conditions.

Contribution

It introduces a new definition of null hypersurfaces in degenerate space-times and proves the conjecture that phase boundaries are null in this context.

Findings

Phase boundaries are null in certain degenerate space-times.

New definition of null hypersurfaces in degenerate space-times.

Supports the conjecture about the nature of phase boundaries.

Abstract

Timelike and null hypersurfaces in the degenerate space-times in the Ashtekar theory are defined in the light of the degenerate causal structure proposed by Matschull. Using the new definition of null hypersufaces, the conjecture that the "phase boundary" separating the degenerate space-time region from the non-degenerate one in Ashtekar's gravity is always null is proved under certain circumstances.