Curved branes with regular support
  We study spacetime singularities in a general five-dimensional braneworld with curved branes satisfying four-dimensional maximal symmetry. The bulk is supported by an analog of perfect fluid with the time replaced by the extra coordinate. We show that contrary to the existence of finite distance singularities from the brane location in any solution with flat (Minkowski) branes, in the case of curved branes there are singularity-free solutions for a range of equations of state compatible with the null energy condition. 
Ignatios Antoniadis, Spiros Cotsakis, Ifigeneia Klaoudatou
hep-th gr-qc