Geodesics and Newton’s law in brane backgrounds

Abstract

In brane world models our universe is considered as a brane imbedded into a higher dimensional space. We discuss the behaviour of geodesics in the Randall-Sundrum background and point out that free massive particles cannot move along the brane only. The brane is repulsive, and matter will be expelled from the brane into the extra dimension. This is rather undesirable, and hence we study an alternative model with a non-compact extra dimension, but with an attractive brane embedded into the higher dimensional space. We study the linearized gravity equations and show that Newton's gravitational law is valid on the brane also in the alternative background. *

Complementarity of the Maldacena and Randall-Sundrum Pictures

“…We shall confirm below that a more careful analysis of the Randall-Sundrum picture using the results of [9,17] yields exactly the same answer as the above AdS/CFT calculation, thus providing strong evidence for the conjectured duality of the two pictures. First we derive (4) in more detail by computing the lowest order quantum corrections to solutions of Einstein's equations.…”

Recovery of the Schwarzschild metric in theories with localized gravity beyond linear order

“…Indeed, as it was pointed out in [10], all material particles fall freely towards the AdS 5 horizon. Additional non-gravitational mechanisms are required to stabilize the brane and confine all material particles within the brane.…”

Consistent linearized gravity in brane backgrounds

“…Our motivation for studying the alternative background is that the brane attracts ordinary matter in that case, whereas it is repulsive in the Randall-Sundrum case [28]. Consistency of our calculation is made possible by adopting a novel gauge fixing (cf.…”

“…In particular, a non-gravitational mechanism of confinement for the RS background turns out to be essential not only because of the instability of the geodesics on the brane [28,37], but also for the Newtonian dynamics on the brane, which would be spoiled by extrinsic contributions. On the other hand, Einstein's equation does not hold for long distances for the alternative background.…”