Spherically symmetric braneworld solutions with an ( 4 ) R term in the bulk

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-$(\mathrm{A}){\mathrm{dS}}_{4}$ form. Two modified Oppenheimer-Volkoff interior solutions are also found; one is matched to a Schwarzschild-$(\mathrm{A}){\mathrm{dS}}_{4}$ exterior, while the other is not. A nonuniversal gravitational constant arises, depending on the density of the considered object; however, the conventional limits of 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 the usual brane dynamics, this string scale is calculated to be larger than TeV.