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Quasinormal Modes of C-metric from SCFTs

Yang Lei, Hongfei Shu, Kilar Zhang, Rui-Dong Zhu

Abstract

We study the quasinormal modes (QNM) of the charged C-metric, which physically stands for a charged accelerating black hole, with the help of Nekrasov's partition function of 4d $\mathcal{N}=2$ superconformal field theories (SCFTs). The QNM in the charged C-metric are classified into three types: the photon-surface modes, the accelerating modes and the near-extremal modes, and it is curious how the single quantization condition proposed in arXiv:2006.06111 can reproduce all the different families. We show that the connection formula encoded in terms of Nekrasov's partition function captures all these families of QNM numerically and recovers the asymptotic behavior of the accelerating and the near-extremal modes analytically. Using the connection formulae of different 4d $\mathcal{N}=2$ SCFTs, one can solve both the radial and the angular part of the scalar perturbation equation respectively. The same algorithm can be applied to the de Sitter (dS) black holes to calculate both the dS modes and the photon-sphere modes.

Quasinormal Modes of C-metric from SCFTs

Abstract

We study the quasinormal modes (QNM) of the charged C-metric, which physically stands for a charged accelerating black hole, with the help of Nekrasov's partition function of 4d superconformal field theories (SCFTs). The QNM in the charged C-metric are classified into three types: the photon-surface modes, the accelerating modes and the near-extremal modes, and it is curious how the single quantization condition proposed in arXiv:2006.06111 can reproduce all the different families. We show that the connection formula encoded in terms of Nekrasov's partition function captures all these families of QNM numerically and recovers the asymptotic behavior of the accelerating and the near-extremal modes analytically. Using the connection formulae of different 4d SCFTs, one can solve both the radial and the angular part of the scalar perturbation equation respectively. The same algorithm can be applied to the de Sitter (dS) black holes to calculate both the dS modes and the photon-sphere modes.
Paper Structure (34 sections, 187 equations, 3 figures, 13 tables)

This paper contains 34 sections, 187 equations, 3 figures, 13 tables.

Table of Contents

  1. Introduction
  2. Quantized Seiberg-Witten approach to QNM
  3. Quasinormal modes of black holes
  4. Seiberg Witten curve and its quantization
  5. AGT duality to conformal blocks
  6. WKB approach and quantization conditions
  7. QNM in the charged C-metric
  8. Dictionary between BH data and SW data
  9. An apparent puzzle in the B-cycle quantization
  10. Connection formula approach to QNM
  11. Connection formula and numerical results
  12. Remark:
  13. Analytical results on QNM
  14. QNM in small $\alpha M$ region
  15. QNM in the near-extremal region
  16. ...and 19 more sections

Figures (3)

  • Figure 1: The A-cycle and B-cycle as classically allowed and forbidden regions in quantum mechanics.
  • Figure 2: The boundary condition of C-metric geometry.
  • Figure 3: The plot of $1/|A_{-+}|$ on the plane of $\omega=x-iy$ including 3-instanton corrections with the spikes (poles) corresponding to QNM in the charged C-metric.