Self-adjoint extensions and Signature Change

TL;DR

This paper investigates the self-adjoint extensions of the spatial D'Alembert operator in spacetimes with signature change, identifying boundary conditions that challenge the idea of signature change regions isolating singularities.

Contribution

It characterizes boundary conditions for the operator in signature-changing spacetimes, providing insights into their implications for singularity isolation.

Findings

Boundary conditions parametrized by U(2) matrices are identified.

Signature change regions do not necessarily isolate singularities.

The study challenges previous suggestions about signature change and singularities.

Abstract

We study the selfadjoint extensions of the spatial part of the D'Alembert operator in a spacetime with two changes of signature. We identify a set of boundary conditions, parametrised by U(2) matrices, which correspond to Dirichlet boundary conditions for the fields, and from which we argue against the suggestion that regions of signature change can isolate singularities.