  The interior of a static Schwarzschild metric can be written in terms of two
functions, similar to some models of anisotropic cosmology. With a suitable
choice of canonical variables, we solve the Wheeler-DeWitt equation (WDW)
inside the horizon of a Schwarzschild black hole. By imposing classicality near
the horizon, and requiring boundedness of the wave function, we get a rather
generic solution of the WDW equation, whose steepest-descent solution, i.e.,
the ridge of the wave function, coincides nicely with the classical trajectory.
However, there is an ambiguity in defining the arrow of time which leads to two
possible interpretations - (i) if there is only one arrow of time, one can
infer that the steepest-descent of the wave function follows the classical
trajectory throughout: coming from the event horizon and going all the way down
to the singularity, while (ii) if there are two different arrows of time in two
separate regimes, it can be inferred that the steepest-descent of the wave
function comes inwards from the event horizon in one region while it moves
outwards from the singularity in the other region, and there exists an
annihilation process of these two parts of the wave function inside the
horizon. Adopting the second interpretation could shed light on the information
loss paradox: as time goes on, probabilities for histories that include black
holes and singularities decay to zero and eventually only trivial geometries
dominate.
