Spherically Symmetric Braneworld Solutions with R_{4} term in the Bulk

TL;DR

This paper investigates spherically symmetric braneworld solutions with an R_{4} term in the bulk, deriving various exterior and interior solutions, analyzing gravitational constants, and setting bounds on the string scale based on solar system data.

Contribution

It provides new solutions for braneworld configurations with an R_{4} term, including modified interior and exterior metrics, and explores implications for gravitational constants and string scale bounds.

Findings

Solutions include Schwarzschild-(A)dS_{4} forms outside matter

Two modified Oppenheimer-Volkoff interior solutions are found

An upper bound of TeV for the string scale is derived from solar system tests

Abstract

An analysis of a spherically symmetric braneworld configuration is performed when the intrinsic curvature scalar is included in the bulk action; the vanishing of the electric part of the Weyl tensor is used as the boundary condition for the embedding of the brane in the bulk. All the solutions outside a static localized matter distribution are found; some of them are of the Schwarzschild-(A)dS_{4} form. Two modified Oppenheimer-Volkoff interior solutions are also found; one is matched to a Schwarzschild-(A)dS_{4} exterior, while the other does not. A non-universal gravitational constant arises, depending on the density of the considered object; however, the conventional limits of the Newton's constant are recovered. An upper bound of the order of TeV for the energy string scale is extracted from the known solar system measurements (experiments). On the contrary, in usual brane dynamics, this string scale is calculated to be larger than TeV.