Geodesics, the Equivalence Principle and Singularities in Higher-dimensional General Relativity and Braneworlds

TL;DR

This paper explores how geodesics differ between higher-dimensional spacetimes and embedded submanifolds, analyzing implications for the equivalence principle and singularities in braneworld models.

Contribution

It provides a detailed investigation of geodesic behavior in higher-dimensional models, including asymmetric braneworlds, and assesses their impact on fundamental principles and singularities.

Findings

Geodesics often do not coincide between the bulk and submanifold.

Symmetric $Z_2$ braneworlds with negative cosmological constant are favored.

Results have implications for the equivalence principle and cosmological singularities.

Abstract

The geodesics of a spacetime seldom coincide with those of an embedded submanifold of codimension one. We investigate this issue for higher-dimensional general relativity-like models, firstly in the simpler case without branes to isolate which features are already present, and then in the more complicated case with branes. The framework in which we consider branes is general enough to include asymmetric braneworlds but not thick branes. We apply our results on geodesics to study both the equivalence principle and cosmological singularities. Among the models we study these considerations favour $Z_2$ symmetric braneworlds with a negative bulk cosmological constant.