Intersecting hypersurfaces and Lovelock Gravity

TL;DR

This paper explores the behavior of intersecting hypersurfaces within Lovelock gravity, revealing the possibility of matter localization at intersections, which is not possible in standard Einstein-Hilbert gravity, thus providing insights relevant to string theory models.

Contribution

It demonstrates that in Lovelock gravity, intersecting hypersurfaces can host localized matter with mild curvature singularities, extending the understanding of brane intersections beyond Einstein gravity.

Findings

Exact thin shells of matter are possible with mild curvature singularities.

Matter can be localized at intersections of hypersurfaces in Lovelock gravity.

Such phenomena do not occur in pure Einstein-Hilbert gravity.

Abstract

A theory of gravity in higher dimensions is considered. The usual Einstein-Hilbert action is supplemented with Lovelock terms, of higher order in the curvature tensor. These terms are important for the low energy action of string theories. The intersection of hypersurfaces is studied in the Lovelock theory. The study is restricted to hypersurfaces of co-dimension 1, $(d-1)$-dimensional submanifolds in a $d$-dimensional space-time. It is found that exact thin shells of matter are admissible, with a mild form of curvature singularity: the first derivative of the metric is discontinuous across the surface. Also, with only this mild kind of curvature singularity, there is a possibility of matter localised on the intersections. This gives a classical analogue of the intersecting brane-worlds in high energy String phenomenology. Such a possibility does not arise in the pure Einstein-Hilbert case.