Newton's law in braneworlds with an infinite extra dimension

TL;DR

This paper investigates how Newton's law behaves in warped braneworld models with one infinite extra dimension and multiple compactified dimensions, deriving explicit corrections to gravity.

Contribution

It provides an exact derivation of Newton's law correction in a braneworld with one infinite and multiple compactified extra dimensions, using Bessel functions.

Findings

Wave function of gravity described by Bessel functions

Explicit correction to Newton's law for n=1

General framework for n extra compactified dimensions

Abstract

We study the behavior of the four$-$dimensional Newton's law in warped braneworlds. The setup considered here is a $(3+n)$-brane embedded in $(5+n)$ dimensions, where $n$ extra dimensions are compactified and a dimension is infinite. We show that the wave function of gravity is described in terms of the Bessel functions of $(2+n/2)$-order and that estimate the correction to Newton's law. In particular, the Newton's law for $n=1$ can be exactly obtained.