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

TL;DR

This paper models a warped six-dimensional universe with an extra two-dimensional sphere, deriving a gravitational potential that combines Newtonian gravity with Yukawa corrections from Kaluza-Klein modes, providing insights into gravity's behavior in higher dimensions.

Contribution

It presents a solvable 6D warped model with an arbitrary energy-momentum tensor, deriving the gravitational potential including KK mode corrections, and demonstrating the potential's behavior near small distances.

Findings

Gravitational potential includes infinite Yukawa series from KK modes.

Series converges to a $1/r^3$ behavior near $r=0$.

Model is applicable to general bulk matter without specific field choices.

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 $r=0$.