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PreprintCC BY 4.0arXiv

Can one hear the shape of a black hole singularity?

  • Sean A. Hartnoll
  • Alexander Zhiboedov
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Abstract

We compute the large overtone quasinormal frequencies ωn of asymptotically AdS black holes with interior near-singularity Kasner epochs. We show that the Kasner exponents can be extracted cleanly from the large n behaviour of the dispersion ∂ ωn/∂ k2 at k=0, where k is a boundary momentum. We show that Kasner transitions, as occur in BKL near-singularity chaos, are audible in the quasinormal frequencies and reveal a map between overtone number n and proper time to the singularity. Our results are obtained using a WKB analysis that isolates non-analytic exponents, determined by the near-singularity spacetime, from non-universal data such as the optical distance from the boundary to the singularity. We check our formulae in several numerical models.

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Cite

BibTeXRIS
BibTeX
@misc{hartnoll2026hear,
  title = {{Can one hear the shape of a black hole singularity?}},
  author = {Sean A. Hartnoll and Alexander Zhiboedov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07514},
  eprint = {2609.07514},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07514},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Can one hear the shape of a black hole singularity?
AU  - Sean A. Hartnoll
AU  - Alexander Zhiboedov
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07514
UR  - https://arxiv.org/abs/2609.07514
AB  - We compute the large overtone quasinormal frequencies ω_n of asymptotically AdS black holes with interior near-singularity Kasner epochs. We show that the Kasner exponents can be extracted cleanly from the large n behaviour of the dispersion ∂ ω_n/∂ k^2 at k=0, where k is a boundary momentum. We show that Kasner transitions, as occur in BKL near-singularity chaos, are audible in the quasinormal frequencies and reveal a map between overtone number n and proper time to the singularity. Our results are obtained using a WKB analysis that isolates non-analytic exponents, determined by the near-singularity spacetime, from non-universal data such as the optical distance from the boundary to the singularity. We check our formulae in several numerical models.
ER  -