Geodesics, the equivalence principle and singularities in higher-dimensional generalrelativity and braneworlds

Abstract

The geodesics of a spacetime seldom coincide with those of an embedded submanifold ofco-dimension one. We investigate this issue for higher-dimensional general relativity-likemodels, firstly in the simpler case without branes to isolate which features are alreadypresent, and then in the more complicated case with branes. The framework in which weconsider branes is general enough to include asymmetric braneworlds but not thick branes.We apply our results on geodesics to study both the equivalence principle andcosmological singularities. Among the models that we study, these considerations favourZ2 symmetric braneworlds with a negative bulk cosmological constant.