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Peer-reviewedCC BY 4.0The European Physical Journal C

Near-horizon deformation of metric and the black hole instability

  • Shi-Jie Ma1
  • Zhan-Feng Mai2
  • Run-Qiu Yang1
  1. 1Tianjin University
  2. 2Guangxi University
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Abstract

Recent time-domain analyses suggest that black hole stability may be sensitive to localized near-horizon geometric deformations, while the underlying spectral mechanism remain unclear. In this work, after verifying the instability of the model in the time domain, we systematically investigate quasi-normal mode spectra under static localized non-positive perturbations within a frequency-domain framework. We find that such deformations generically induce a new purely imaginary mode. As the deformation approaches the horizon, the imaginary part of this mode increases and eventually enters the upper half complex-frequency plane, signaling the onset of black hole instability. Numerical results reveal clear scaling relations between the critical distance for instability and the deformation strength. We further derive rigorous proofs for our discoveries in frequency domain. These results demonstrate that black hole stability under long scale is conditionally sensitive to localized deformation of metric near the horizon and establish a unified spectral framework for understanding their induced instabilities.

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Cite

BibTeXRIS
BibTeX
@article{ma2026nearhorizon,
  title = {{Near-horizon deformation of metric and the black hole instability}},
  author = {Shi-Jie Ma and Zhan-Feng Mai and Run-Qiu Yang},
  journal = {The European Physical Journal C},
  year = {2026},
  month = oct,
  doi = {10.1140/epjc/s10052-026-16424-2},
  url = {https://link.springer.com/10.1140/epjc/s10052-026-16424-2},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Near-horizon deformation of metric and the black hole instability
AU  - Shi-Jie Ma
AU  - Zhan-Feng Mai
AU  - Run-Qiu Yang
PY  - 2026
DA  - 2026/10/07
JO  - The European Physical Journal C
DO  - 10.1140/epjc/s10052-026-16424-2
UR  - https://link.springer.com/10.1140/epjc/s10052-026-16424-2
AB  - Recent time-domain analyses suggest that black hole stability may be sensitive to localized near-horizon geometric deformations, while the underlying spectral mechanism remain unclear. In this work, after verifying the instability of the model in the time domain, we systematically investigate quasi-normal mode spectra under static localized non-positive perturbations within a frequency-domain framework. We find that such deformations generically induce a new purely imaginary mode. As the deformation approaches the horizon, the imaginary part of this mode increases and eventually enters the upper half complex-frequency plane, signaling the onset of black hole instability. Numerical results reveal clear scaling relations between the critical distance for instability and the deformation strength. We further derive rigorous proofs for our discoveries in frequency domain. These results demonstrate that black hole stability under long scale is conditionally sensitive to localized deformation of metric near the horizon and establish a unified spectral framework for understanding their induced instabilities.
SN  - 1434-6044
SN  - 1434-6052
ER  -