Newton's law on an Einstein "Gauss-Bonnet" brane

It is known that Newton's law of gravity holds asymptotically on a flat "brane" embedded in an anti-de Sitter "bulk" ; this was shown not only when gravity in the bulk is described by Einstein's theory but also in Einstein "Lanczos Lovelock Gauss-Bonnet"'s theory. We give here the expressions for the corrections to Newton's potential in both theories, in analytic form and valid for all distances. We find that in Einstein's theory the transition from the 1/r behaviour at small r to the 1/r^2 one at large r is quite slow. In the Einstein Gauss-Bonnet case on the other hand, we find that the correction to Newton's potential can be small for all r. Hence, Einstein Gauss-Bonnet equations in the bulk (rather than simply Einstein's) induce on the brane a better approximation to Newton's law.Comment: typos corrected, reference added, version to be published in Progress of Theoretical Physic

Collapsing sphere on the brane radiates

We study the analogue of the Oppenheimer-Snyder model of a collapsing sphere of homogeneous dust on the Randall-Sundrum type brane. We show that the collapsing sphere has the Vaidya radiation envelope which is followed by the brane analogue of the Schwarzschild solution described by the Reissner-Nordstrom metric. The collapsing solution is matched to the brane generalized Vaidya solution and which in turn is matched to the Reissner-Nordstrom metric. The mediation by the Vaidya radiation zone is the new feature introduced by the brane. Since the radiating mediation is essential, we are led to the remarkable conclusion that a collapsing sphere on the brane does indeed, in contrast to general relativity, radiate null radiation.Comment: Minor changes, main results remain unchanged, to appear in Phys. Lett.