  We develop an extension of Bohmian mechanics to a curved background
space-time containing a singularity. The present paper focuses on timelike
singularities. We use the naked timelike singularity of the super-critical
Reissner-Nordstrom geometry as an example. While one could impose boundary
conditions at the singularity that would prevent the particles from falling
into the singularity, we are interested here in the case in which particles
have positive probability to hit the singularity and get annihilated. The wish
for reversibility, equivariance, and the Markov property then dictates that
particles must also be created by the singularity, and indeed dictates the rate
at which this must occur. That is, a stochastic law prescribes what comes out
of the singularity. We specify explicit equations of a non-rigorous model
involving an interior-boundary condition on the wave function at the
singularity, which can be used also in other versions of quantum theory besides
Bohmian mechanics. As the resulting theory involves particle creation and
annihilation, it can be regarded as a quantum field theory, and the stochastic
process for the Bohmian particles is analogous to Bell-type quantum field
theories.
