---
OA_place: repository
_id: '19552'
abstract:
- lang: eng
  text: "Particle creation terms in quantum Hamiltonians are usually ultraviolet\r\ndivergent
    and thus mathematically ill defined. A rather novel way of solving\r\nthis problem
    is based on imposing so-called interior-boundary conditions on the\r\nwave function.
    Previous papers showed that this approach works in the\r\nnon-relativistic regime,
    but particle creation is mostly relevant in the\r\nrelativistic case after all.
    In flat relativistic space-time (that is,\r\nneglecting gravity), the approach
    was previously found to work only for certain\r\nsomewhat artificial cases. Here,
    as a way of taking gravity into account, we\r\nconsider curved space-time, specifically
    the super-critical\r\nReissner-Nordstr\\\"om space-time, which features a naked
    timelike singularity.\r\nWe find that the interior-boundary approach works fully
    in this setting; in\r\nparticular, we prove rigorously the existence of well-defined,
    self-adjoint\r\nHamiltonians with particle creation at the singularity, based
    on\r\ninterior-boundary conditions. We also non-rigorously analyze the asymptotic\r\nbehavior
    of the Bohmian trajectories and construct the corresponding Bohm-Bell\r\nprocess
    of particle creation, motion, and annihilation. The upshot is that in\r\nquantum
    physics, a naked space-time singularity need not lead to a breakdown of\r\nphysical
    laws, but on the contrary allows for boundary conditions governing\r\nwhat comes
    out of the singularity and thereby removing the ultraviolet\r\ndivergence."
acknowledgement: "JH gratefully acknowledges partial financial support by the ERC
  Advanced\r\nGrant “RMTBeyond” No. 101020331."
article_processing_charge: No
arxiv: 1
author:
- first_name: Sven Joscha
  full_name: Henheik, Sven Joscha
  id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
  last_name: Henheik
  orcid: 0000-0003-1106-327X
- first_name: Bipul
  full_name: Poudyal, Bipul
  last_name: Poudyal
- first_name: Roderich
  full_name: Tumulka, Roderich
  last_name: Tumulka
citation:
  ama: Henheik SJ, Poudyal B, Tumulka R. How a space-time singularity helps remove
    the ultraviolet divergence problem. <i>arXiv</i>. doi:<a href="https://doi.org/10.48550/arXiv.2409.00677">10.48550/arXiv.2409.00677</a>
  apa: Henheik, S. J., Poudyal, B., &#38; Tumulka, R. (n.d.). How a space-time singularity
    helps remove the ultraviolet divergence problem. <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.2409.00677">https://doi.org/10.48550/arXiv.2409.00677</a>
  chicago: Henheik, Sven Joscha, Bipul Poudyal, and Roderich Tumulka. “How a Space-Time
    Singularity Helps Remove the Ultraviolet Divergence Problem.” <i>ArXiv</i>, n.d.
    <a href="https://doi.org/10.48550/arXiv.2409.00677">https://doi.org/10.48550/arXiv.2409.00677</a>.
  ieee: S. J. Henheik, B. Poudyal, and R. Tumulka, “How a space-time singularity helps
    remove the ultraviolet divergence problem,” <i>arXiv</i>. .
  ista: Henheik SJ, Poudyal B, Tumulka R. How a space-time singularity helps remove
    the ultraviolet divergence problem. arXiv, <a href="https://doi.org/10.48550/arXiv.2409.00677">10.48550/arXiv.2409.00677</a>.
  mla: Henheik, Sven Joscha, et al. “How a Space-Time Singularity Helps Remove the
    Ultraviolet Divergence Problem.” <i>ArXiv</i>, doi:<a href="https://doi.org/10.48550/arXiv.2409.00677">10.48550/arXiv.2409.00677</a>.
  short: S.J. Henheik, B. Poudyal, R. Tumulka, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-04-11T12:07:25Z
date_published: 2025-02-28T00:00:00Z
date_updated: 2026-04-07T12:37:11Z
day: '28'
department:
- _id: LaEr
doi: 10.48550/arXiv.2409.00677
ec_funded: 1
external_id:
  arxiv:
  - '2409.00677'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2409.00677
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: arXiv
publication_status: draft
related_material:
  record:
  - id: '19540'
    relation: dissertation_contains
    status: public
status: public
title: How a space-time singularity helps remove the ultraviolet divergence problem
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2025'
...