@unpublished{19552,
  abstract     = {Particle creation terms in quantum Hamiltonians are usually ultraviolet
divergent and thus mathematically ill defined. A rather novel way of solving
this problem is based on imposing so-called interior-boundary conditions on the
wave function. Previous papers showed that this approach works in the
non-relativistic regime, but particle creation is mostly relevant in the
relativistic case after all. In flat relativistic space-time (that is,
neglecting gravity), the approach was previously found to work only for certain
somewhat artificial cases. Here, as a way of taking gravity into account, we
consider curved space-time, specifically the super-critical
Reissner-Nordstr\"om space-time, which features a naked timelike singularity.
We find that the interior-boundary approach works fully in this setting; in
particular, we prove rigorously the existence of well-defined, self-adjoint
Hamiltonians with particle creation at the singularity, based on
interior-boundary conditions. We also non-rigorously analyze the asymptotic
behavior of the Bohmian trajectories and construct the corresponding Bohm-Bell
process of particle creation, motion, and annihilation. The upshot is that in
quantum physics, a naked space-time singularity need not lead to a breakdown of
physical laws, but on the contrary allows for boundary conditions governing
what comes out of the singularity and thereby removing the ultraviolet
divergence.},
  author       = {Henheik, Sven Joscha and Poudyal, Bipul and Tumulka, Roderich},
  booktitle    = {arXiv},
  title        = {{How a space-time singularity helps remove the ultraviolet divergence problem}},
  doi          = {10.48550/arXiv.2409.00677},
  year         = {2025},
}