Gravity in a warped 6D world with an extra 2D sphere

Abstract

Corrections to Newton's inverse law have been so far considered, but not clear in warped higher dimensional worlds, because of complexity of the Einstein equation. Here we give a model of a warped 6D world with an extra 2D sphere. We take a general energy-momentum tensor, which does not depend on a special choice of bulk matter fields. The 6D Einstein equation reduces to the spheroidal differential equation, which can be easily solved. The gravitational potential in our 4D universe is calculated to be composed of infinite series of massive Yukawa potentials coming from the KK mode, together with Newton's inverse law. The series of Yukawa type potentials converges well to behave as $1/r^3$ near $r=0$.