Curvature Reconstruction and Tensor Polarizations in Isospectrality-Breaking Black-Hole Perturbations
Abstract
Testing general relativity with the ringdown phase of gravitational waves requires connecting modifications of black-hole perturbation dynamics to observable signatures in detector strain. In this work, we study the relation between curvature perturbations, metric master variables, and detector tensor polarizations for nonrotating black holes in dynamical Chern-Simons gravity. In this theory the axial gravitational perturbation couples to a dynamical scalar field, while the polar sector remains GR-like at the order considered. We first construct a map for the perturbed Weyl scalar δΨ0, expressing its even-parity part in terms of the ZM master function and its odd-parity part in terms of the RW master function together with the scalar radial perturbation. We also derive the leading asymptotic tensor polarizations h+ and h× directly from the metric perturbations. The resulting strain is reconstructed from the radiative gravitational master functions: the ZM function in the even sector and the Cunningham-Price-Moncrief-normalized odd function in the axial sector for dynamical Chern-Simons gravity. No independent local algebraic term proportional to the scalar radial function appears in the leading tensor strain. These results separate curvature-level scalar dependence from tensor-channel scalar-frequency responses and provide the formal reconstruction basis for companion work on parity-split beating and effective ringdown frequencies.
Related
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- Isospectrality breaking in the axial quasinormal modes of Reissner-Nordström black holes in dynamical Chern-Simons gravity
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- How do late-time photons "record" primordial curvature perturbations?
- Enabling Polyspectra via Stochastic Realizations of Inverse Decay Curvature Perturbations in Axion Inflation
BibTeX
@misc{wagle2026curvature,
title = {{Curvature Reconstruction and Tensor Polarizations in Isospectrality-Breaking Black-Hole Perturbations}},
author = {Pratik Wagle and Dongjun Li and Yanbei Chen and Nicolas Yunes},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27116},
eprint = {2610.27116},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27116},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Curvature Reconstruction and Tensor Polarizations in Isospectrality-Breaking Black-Hole Perturbations
AU - Pratik Wagle
AU - Dongjun Li
AU - Yanbei Chen
AU - Nicolas Yunes
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27116
UR - https://arxiv.org/abs/2610.27116
AB - Testing general relativity with the ringdown phase of gravitational waves requires connecting modifications of black-hole perturbation dynamics to observable signatures in detector strain. In this work, we study the relation between curvature perturbations, metric master variables, and detector tensor polarizations for nonrotating black holes in dynamical Chern-Simons gravity. In this theory the axial gravitational perturbation couples to a dynamical scalar field, while the polar sector remains GR-like at the order considered. We first construct a map for the perturbed Weyl scalar δΨ_0, expressing its even-parity part in terms of the ZM master function and its odd-parity part in terms of the RW master function together with the scalar radial perturbation. We also derive the leading asymptotic tensor polarizations h_+ and h_× directly from the metric perturbations. The resulting strain is reconstructed from the radiative gravitational master functions: the ZM function in the even sector and the Cunningham-Price-Moncrief-normalized odd function in the axial sector for dynamical Chern-Simons gravity. No independent local algebraic term proportional to the scalar radial function appears in the leading tensor strain. These results separate curvature-level scalar dependence from tensor-channel scalar-frequency responses and provide the formal reconstruction basis for companion work on parity-split beating and effective ringdown frequencies.
ER -