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The singularity structure and the corresponding asymptotic behavior of a3-brane coupled to a scalar field or to a perfect fluid in a five-dimensionalbulk is analyzed in full generality using the method of asymptotic splittings.In the case of the scalar field, it is shown that the collapse singularity at afinite distance from the brane can be avoided only at the expense of making thebrane world-volume positively or negatively curved. In the case where the bulkfield content is parametrized by an analogue of perfect fluid with an arbitraryequation of state P=\gamma\rho between the `pressure' P and the `density' \rho,our results depend crucially on the constant fluid parameter \gamma: (i) For\gamma>-1/2, the flat brane solution suffers from a collapse singularity atfinite distance, that disappears in the curved case. (ii) For \gamma<-1, thesingularity cannot be avoided and it becomes of the big rip type for a flatbrane. (iii) For -1<\gamma< or = -1/2, the surprising result is found thatwhile the curved brane solution is singular, the flat brane is not, opening thepossibility for a revival of the self-tuning proposal.

Brane singularities and their avoidance