Newton Law on the Generalized Singular Brane with and without 4d Induced Gravity

TL;DR

This paper investigates how Newton's law manifests on various singular branes in an AdS_5 bulk, analyzing the effects of induced gravity terms and boundary conditions on gravitational behavior at different scales.

Contribution

It provides a detailed analysis of Newtonian potential behavior on different branes with and without induced Einstein terms, highlighting new effects of boundary conditions and coupling constants.

Findings

On RS brane, Newton potential exhibits 4d and 5d behavior at different ranges.

Induced Einstein term creates an intermediate range with 5d Newtonian behavior.

On Neumann brane, long-range Newton potential is exponentially suppressed.

Abstract

Newton law arising due to the gravity localized on the general singular brane embedded in $AdS_5$ bulk is examined in the absence or presence of the 4d induced Einstein term. For the RS brane, apart from the subleading correction, Newton potential obeys 4d-type and $5d$-type gravitational law at long- and short-ranges if it were not for the induced Einstein term. The 4d induced Einstein term generates an intermediate range at short distance, in which the $5d$ Newton potential $1/r^2$ emerges. For Neumann brane the long-range behavior of Newton potential is exponentially suppressed regardless of the existence of the induced Einstein term. For Dirichlet brane the expression of Newton potential is dependent on the renormalized coupling constant $v^{ren}$. At particular value of $v^{ren}$ Newton potential on Dirichlet brane exhibits a similar behavior to that on RS brane. For other values the long-range behavior of Newton potential is exponentially suppressed as that in Neumann brane.