Singularity avoidance from path integral

Abstract

We have demonstrated that the wave functional describing the quantum nature of the spacetime inside the black hole horizon, vanishes near the singularity, using the path integral formalism. This is akin to the DeWitt criterion, applied to the interior of a Schwarzschild black hole. To achieve the same we have expressed the interior of a Schwarzschild black hole as a Kantowski-Sachs spacetime and have applied the minisuperspace formalism to determine an exact form of the propagator, and hence the wave function near the singularity, using path integral over the reduced phase space. It is to be emphasized that our result is exact and not a saddle point approximation to the path integral.