Transition from Big Crunch to Big Bang in Brane Cosmology

We consider a brane N = I × S0, where S0 is an ndimensional space form, not necessarily compact, in a SchwarzschildAdS(n+2) bulk N and prove that, for specific negative pressures on the brane, the brane is an ARW space. By reflecting N and N to N̂ and N̂ , the joint branes N ∪ N̂ can be naturally embedded as a C∞hypersurface in R2 ×S0, if n is odd and if ω = − n−1 2 is chosen, a value that corresponds to the assumption of a radiation dominated universe in classical general relativity. We also consider branes that are not ARW spaces and prove for a wide range of ω, even variable ω, that N ∪ N̂ is a C∞-hypersurface in