Degenerate Metric Phase Boundaries

TL;DR

This paper investigates the boundaries between degenerate and nondegenerate solutions in Ashtekar's formulation of Einstein's equations, revealing null phase boundaries with examples from various spacetime solutions.

Contribution

It introduces the concept of degenerate metric phase boundaries, provides explicit examples, and conjectures their null nature within the context of Ashtekar's formalism.

Findings

Examples include flat space, Schwarzschild, and plane wave solutions.

Degenerate phase boundaries are likely always null.

Wave collision with a phase boundary preserves curvature.

Abstract

The structure of boundaries between degenerate and nondegenerate solutions of Ashtekar's canonical reformulation of Einstein's equations is studied. Several examples are given of such "phase boundaries" in which the metric is degenerate on one side of a null hypersurface and non-degenerate on the other side. These include portions of flat space, Schwarzschild, and plane wave solutions joined to degenerate regions. In the last case, the wave collides with a planar phase boundary and continues on with the same curvature but degenerate triad, while the phase boundary continues in the opposite direction. We conjecture that degenerate phase boundaries are always null.