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–Nordström metric. The collapsing solution is matched to the brane generalized Vaidya solution and which in turn is matched to the Reissner–Nordström 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.