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Hawking Amplitudes: Subtle Points About Saddle Points

  • Owen Lear
  • Daniel McLoughlin
  • Sebastian Mizera
  • John Staunton
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Abstract

Hawking amplitudes provide a new way of determining the Hawking spectrum of black holes, using on-shell techniques borrowed from the literature on scattering amplitudes. In this paper, we investigate the interplay between the semi-classical and weak-field approximations previously used to compute Hawking amplitudes. We find that these limits do not necessarily commute, highlighting subtleties with the saddle point analyses governing the semi-classical limit. Resolving these issues allows us to compute semi-classical Hawking amplitudes in a range of black-hole backgrounds, including Tangherlini, Reissner-Nordström, and Hernquist metrics. Moreover, we describe the saddle-point contributions dominating Hawking amplitudes for different energies and propose a new method for determining the temperature of the resulting thermal spectrum based on Stokes lines of Hawking amplitudes.

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Cite

BibTeXRIS
BibTeX
@misc{lear2026hawking,
  title = {{Hawking Amplitudes: Subtle Points About Saddle Points}},
  author = {Owen Lear and Daniel McLoughlin and Sebastian Mizera and John Staunton},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10678},
  eprint = {2610.10678},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10678},
}
RIS
TY  - UNPB
TI  - Hawking Amplitudes: Subtle Points About Saddle Points
AU  - Owen Lear
AU  - Daniel McLoughlin
AU  - Sebastian Mizera
AU  - John Staunton
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10678
UR  - https://arxiv.org/abs/2610.10678
AB  - Hawking amplitudes provide a new way of determining the Hawking spectrum of black holes, using on-shell techniques borrowed from the literature on scattering amplitudes. In this paper, we investigate the interplay between the semi-classical and weak-field approximations previously used to compute Hawking amplitudes. We find that these limits do not necessarily commute, highlighting subtleties with the saddle point analyses governing the semi-classical limit. Resolving these issues allows us to compute semi-classical Hawking amplitudes in a range of black-hole backgrounds, including Tangherlini, Reissner-Nordström, and Hernquist metrics. Moreover, we describe the saddle-point contributions dominating Hawking amplitudes for different energies and propose a new method for determining the temperature of the resulting thermal spectrum based on Stokes lines of Hawking amplitudes.
ER  -