Brane-world stars from minimal geometric deformation, and black holes

Using the effective four-dimensional Einstein field equations, we build analytical models of spherically symmetric stars in the brane-world, in which the external space-time contains both an ADM mass and a tidal charge. In order to deter- mine the interior geometry, we apply the principle of minimal geometric deformation, which allows one to map general relativistic solutions to solutions of the effective four-dimensional brane-world equations. We further restrict our analysis to stars with a radius linearly related to the total general relativistic mass, and obtain a general relation between the latter, the brane-world ADM mass and the tidal charge. In these models, the value of the star’s radius can then be taken to zero smoothly, thus obtaining brane-world black hole metrics with a tidal charge solely determined by the mass of the source and the brane tension. We find configurations which entail a partial screen- ing of the gravitational mass, and general conclusions regarding the minimum mass for semiclassical black holes are also drawn.