Singular Hypersurfaces in Einstein--Gauss--Bonnet Theory of Gravitation

TL;DR

This paper develops a comprehensive formalism for analyzing singular hypersurfaces within Einstein-Gauss-Bonnet gravity, providing generalized junction conditions applicable to various embeddings and matter configurations, with applications to brane cosmology.

Contribution

It introduces a novel, general framework for singular hypersurfaces in Einstein-Gauss-Bonnet gravity, extending previous junction condition formulations.

Findings

Derived generalized junction conditions for singular hypersurfaces.

Applied the formalism to time-like and light-like hypersurfaces in brane cosmology.

Provided a versatile approach for different embeddings and matter contents.

Abstract

We present a general formalism for describing singular hypersurfaces in the Einstein theory of gravitation with a Gauss--Bonnet term. The junction conditions are given in a form which is valid for the most general embedding and matter content and for coordinates chosen independently on each side of the hypersurface. The theory is applied to both a time--like and a light--like hypersurface in brane--cosmology.