Tidal fields on braneworlds

TL;DR

This paper derives the tidal fields experienced on braneworlds within higher-dimensional spacetimes, analyzing how extra dimensions influence geodesic deviations observed in four-dimensional physics.

Contribution

It introduces a method to project higher-dimensional dynamical quantities onto branes, deriving tidal fields in arbitrary extra-dimensional setups using submanifold theory.

Findings

Extra dimensions can cause deviations from standard general relativity tidal effects.

The tidal field depends on the induced metric's variation with extra coordinates.

Deviations arise from higher-dimensional metric asymmetries.

Abstract

We write out the geodesic deviations that take place in a $d\geq 4$ dimensional brane world subspace of a higher dimensional spacetime by splitting out the brane and the extra space dynamical quantities from a global metric spacetime of dimension $D\geq 5$. The higher dimensional dynamical quantities are projected onto two orthogonal subspaces, where one of which is identified with a $(d-1)$-brane. This is done by using some technics of the conventional submanifold theory of the Riemannian geometry, applied to pseudo-Riemannian spaces. Using the splitting technic, we obtain the tidal field on $(d-1)$ branes with an arbitrary number of non compact extra dimensions. Later, we analise the geodesic deviations seen by an ordinary observer in a $d=4$ dimensional spacetime and show that deviations from general relativity tidal field due to the existence of the extra dimensions can appear because, (i) - the dependence of the indunced metric on the brane with the extra coordinates and (ii) - deviations of the higher dimensional spacetime metric from spherical symmetry.