Isospectrality breaking in the axial quasinormal modes of Reissner-Nordström black holes in dynamical Chern-Simons gravity
Abstract
We study odd-parity perturbations of Reissner-Nordström black holes in dynamical Chern-Simons gravity. The dCS action is parity invariant because ϑ *RR is the product of two pseudoscalars; nevertheless, the pseudoscalar perturbation has odd parity and enters only the axial sector at linear order and so lifts the axial--polar isospectrality of general relativity. We derive the finite-charge couplings between the pseudoscalar and the axial gravitational and electromagnetic perturbations directly from the linearized field equations. Both directions are governed by the radial kernel (Mr−Q2)Δ/r8, and at nonzero charge the pseudoscalar couples to Ψ+χΨe, with χ=2Q/[r√((l−1)(l+2))]. After diagonalizing the Einstein--Maxwell sector, we compute branch-resolved quasinormal-mode shifts with exterior complex scaling for the photon-sphere modes and Frobenius shooting for the near-extremal zero-damping modes. For the Schwarzschild l=2 fundamental mode we obtain β δω=−0.7733−0.3946 i (units M=α=1). Off resonance, the gravitational-led shift scales as ζ l3 at Q=0 but as ζ l2/Q at fixed nonzero charge and large l. The electromagnetic-led branch becomes exactly degenerate with the pseudoscalar mode at Qc=2M√(l(l+1)+1)/[l(l+1)+2], where the pseudoscalar potential coincides with the polar partner of the electromagnetic-led potential; there the breaking is 𝒪(√ζ), M|Δω|≃2.4√ζ for l=2, and the shift reverses sign across Qc. Near extremality the photon-sphere shifts remain finite, whereas the non-degenerate fundamental gravitational-led zero-damping mode is suppressed, δω/ω≃6.0×103 ζ (1−Q2/M2) for l=2.
Related
- Nonoscillatory gravitational quasinormal modes of Reissner–Nordström–de Sitter spacetime
- Quasinormal modes of Reissner-Nordström black hole from bound state spectrum
- Quasinormal Modes of Reissner-Nordström Black Holes in Modified Gravity
- Grey-body factor from correspondence with quasinormal mode for gravitational perturbation of higher-dimensional Reissner-Nordström black hole
- Reissner-Nordstrom in the Bertotti-Robinson-Bonnor-Melvin electromagnetic field
BibTeX
@misc{rout2026isospectrality,
title = {{Isospectrality breaking in the axial quasinormal modes of Reissner-Nordström black holes in dynamical Chern-Simons gravity}},
author = {Abhishek Rout},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38742},
eprint = {2610.38742},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38742},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Isospectrality breaking in the axial quasinormal modes of Reissner-Nordström black holes in dynamical Chern-Simons gravity
AU - Abhishek Rout
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38742
UR - https://arxiv.org/abs/2610.38742
AB - We study odd-parity perturbations of Reissner-Nordström black holes in dynamical Chern-Simons gravity. The dCS action is parity invariant because ϑ ^*RR is the product of two pseudoscalars; nevertheless, the pseudoscalar perturbation has odd parity and enters only the axial sector at linear order and so lifts the axial--polar isospectrality of general relativity. We derive the finite-charge couplings between the pseudoscalar and the axial gravitational and electromagnetic perturbations directly from the linearized field equations. Both directions are governed by the radial kernel (Mr−Q^2)Δ/r^8, and at nonzero charge the pseudoscalar couples to Ψ+χΨ_e, with χ=2Q/[r√((l−1)(l+2))]. After diagonalizing the Einstein--Maxwell sector, we compute branch-resolved quasinormal-mode shifts with exterior complex scaling for the photon-sphere modes and Frobenius shooting for the near-extremal zero-damping modes. For the Schwarzschild l=2 fundamental mode we obtain β δω=−0.7733−0.3946 i (units M=α=1). Off resonance, the gravitational-led shift scales as ζ l^3 at Q=0 but as ζ l^2/Q at fixed nonzero charge and large l. The electromagnetic-led branch becomes exactly degenerate with the pseudoscalar mode at Q_c=2M√(l(l+1)+1)/[l(l+1)+2], where the pseudoscalar potential coincides with the polar partner of the electromagnetic-led potential; there the breaking is 𝒪(√ζ), M|Δω|≃2.4√ζ for l=2, and the shift reverses sign across Q_c. Near extremality the photon-sphere shifts remain finite, whereas the non-degenerate fundamental gravitational-led zero-damping mode is suppressed, δω/ω≃6.0×10^3 ζ (1−Q^2/M^2) for l=2.
ER -