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Entropy, area, and the choice of regulator during gravitational collapse

  • Jana N Guenther
  • Christian Hoelbling
  • Sophie Mutzel
  • Lukas Varnhorst
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Abstract

We present a real time formalism to numerically describe the gravitational collapse of a scalar quantum field in the spherically symmetric case. We employ a Pauli-Villars regulator that is specifically designed to cancel the ultraviolet divergences in the energy-momentum tensor identified by covariant point splitting, including the logarithmic ones. Using this regulator, we find that the leading term of the entanglement entropy, which is proportional to the surface area, vanishes for a spherical region of flat spacetime. First numerical results for the dynamical case indicate that for a collapsing shell of a massless scalar field, the area normalized entropy is concentrated on the shell and has an approximately constant maximum value during time evolution. This maximum value appears to be finite in the continuum limit and only mildly dependent on the regulator mass.

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Cite

BibTeXRIS
BibTeX
@misc{guenther2026entropy,
  title = {{Entropy, area, and the choice of regulator during gravitational collapse}},
  author = {Jana N Guenther and Christian Hoelbling and Sophie Mutzel and Lukas Varnhorst},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20663},
  eprint = {2609.20663},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05763259v1},
}
RIS
TY  - UNPB
TI  - Entropy, area, and the choice of regulator during gravitational collapse
AU  - Jana N Guenther
AU  - Christian Hoelbling
AU  - Sophie Mutzel
AU  - Lukas Varnhorst
PY  - 2026
DA  - 2026/09/17
PB  - HAL
DO  - 10.48550/arxiv.2609.20663
UR  - https://hal.science/hal-05763259v1
AB  - We present a real time formalism to numerically describe the gravitational collapse of a scalar quantum field in the spherically symmetric case. We employ a Pauli-Villars regulator that is specifically designed to cancel the ultraviolet divergences in the energy-momentum tensor identified by covariant point splitting, including the logarithmic ones. Using this regulator, we find that the leading term of the entanglement entropy, which is proportional to the surface area, vanishes for a spherical region of flat spacetime. First numerical results for the dynamical case indicate that for a collapsing shell of a massless scalar field, the area normalized entropy is concentrated on the shell and has an approximately constant maximum value during time evolution. This maximum value appears to be finite in the continuum limit and only mildly dependent on the regulator mass.
ER  -