Regular quantum interiors for black holes
  A family of spacetimes suitable for describing the interior of a non-rotational black hole is constructed. The stress-energy tensor is that of a spherically symmetric vacuum, as commonly assumed nowadays. The problem of matching the exterior with the interior region is solved exactly, without using any massive shell nor having to restrict oneself to only asymptotically well-behaved solutions, whatsoever. The main physical and geometrical properties of the resulting black hole solutions are described. As models for the interior the general solution found includes, in particular, two known previous atttempts at solving the problem. Finally, effective macroscopic properties of the solution are linked with quantization issues of the corresponding spacetime. 
Emilio Elizalde and Sergi R. Hildebrandt