Geodesics and Newton’s law in brane backgrounds

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Abstract
In brane world models our universe is considered as a brane embedded into a higher-dimensional space. We discuss the behavior of geodesics in the Randall-Sundrum background and point out that free massive particles cannot stably move along the brane. The brane is repulsive, and matter will be expelled from the brane into the extra dimension. This is undesirable, and hence we study a simple alternative model with a noncompact 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.
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