Application of Colombeau's Generalized Functions to Cosmological Models with Signature Change

TL;DR

This paper applies Colombeau's generalized functions to model singular hypersurfaces with signature change in general relativity, allowing for non-zero stress-energy tensors on the surface.

Contribution

It introduces a novel application of Colombeau's generalized functions to handle signature change in cosmological models, extending the distributional approach.

Findings

Equations for hypersurface dynamics are derived.

Surface stress-energy tensor can be non-zero.

Method enables modeling of signature change in cosmology.

Abstract

Colombeau's generalized functions are used to adapt the distributional approach to singular hypersurfaces in general relativity with signature change. Equations governing the dynamics of singular hypersurface is obtained and it is shown that the stress-energy tensor of the surface can be non-vanishing.