Gravitational odd-parity perturbation of a Horndeski hairy black hole: quasinormal mode and parameter constraint

Abstract

During the binary black hole coalescence, gravitational waves emitted at the ringdown stage can be well described by black hole perturbation theory, where the quasinormal modes (QNMs) become the important ingredient in modeling the pattern waveform. In general relativity (GR), the QNMs can be obtained from solving the Regge-Wheeler (RW) equation of a non-rotating black hole. While in Horndeski gravity, the isospectrality between the odd and even parity perturbations is broken due to the scalar field, but the odd perturbation equation can be simplified into a modified RW equation from the perturbed action. In this paper, we propose a new auxiliary field and tortoise coordinate to refine the modified RW equation in Horndeski gravity, and calculate the QNMs frequencies of the odd perturbation of a specific hairy black hole. It is found that this proposal not only cures the superluminal propagation addressed in the previous literature, but also hold the original QNM spectrum of the odd perturbation. Moreover, our results indicate that such a Horndeski hairy black hole is stable under the odd perturbation, which is also verified by the time evolution of the perturbation. In particular, in contrary to GR, the modes with $\ell =2$ can decay faster than modes with $\ell >2$ for a certain range of the Horndeski hair, and the link between the null geodesics and QNM for the odd perturbation in the current theory is violated. Then, we use the ringdown QNMs to preliminarily investigate the signal-to-noise-ratio (SNR) rescaled measurement error of the Horndeski hair. We obtain significant effects of the angular momentum and overtone on the error bound of the hair parameter. We hope that our findings could inspire more theoretical and phenomenological work on the test of the no-hair theorem of black hole using gravitational wave physics.

V3: New auxiliary field and tortoise coordinate were proposed to cure the superluminal propagation, and the link between the null geodesics and QNM was found to be violated

References in corpus (42)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects
• Horndeski theory and beyond: a review
• Are eikonal quasinormal modes linked to the unstable circular null geodesics?
• Black holes with non-minimal derivative coupling
• Black holes with scalar hair in light of the Event Horizon Telescope
• Probing non-tensorial polarizations of stochastic gravitational-wave backgrounds with ground-based laser interferometers
• Asymptotically locally AdS and flat black holes in the presence of an electric field in the Horndeski scenario
• Testing the no-hair theorem with black hole ringdowns using TIGER
• Ringdown overtones, black hole spectroscopy, and no-hair theorem tests
• No-Hair Theorem in the Wake of Event Horizon Telescope
• Detecting scalar fields with Extreme Mass Ratio Inspirals
• Stability of Schwarzschild-like solutions in f(R,G) gravity models
• Testing Horndeski Gravity from EHT Observational Results for Rotating Black Holes
• Probing vector hair of black holes with extreme mass ratio inspirals
• Linear stability analysis of hairy black holes in quadratic degenerate higher-order scalar-tensor theories: Odd-parity perturbations
• Constraining some Horndeski gravity theories
• Science with the TianQin Observatory: Preliminary Results on Testing the No-hair Theorem with EMRI
• Rings and images of Horndeski hairy black hole illuminated by various thin accretions
• Investigating strong gravitational lensing effects by suppermassive black holes with Horndeski gravity
• Black holes with primary scalar hair
• Rotating Black Holes in Horndeski Gravity: Thermodynamic and Gravitational Lensing
• Existence and Instability of Novel Hairy Black Holes in Shift-symmetric Horndeski Theories
• Building a Holographic Superconductor with a Scalar Field Coupled Kinematically to Einstein Tensor
• Challenges testing the no-hair theorem with gravitational waves
• First-order thermodynamics of Horndeski gravity
• Nonlinear ringdown at the black hole horizon
• On matrix method for black hole quasinormal modes
• Hairy Black Holes: Non-existence of Short Hairs and Bound on Light Ring Size
• Gravitational waves from eccentric extreme mass-ratio inspirals as probes of scalar fields
• Equatorial extreme-mass-ratio inspirals in Kerr black holes with scalar hair spacetimes
• Thermodynamics of Horndeski black holes with non-minimal derivative coupling
• Detection of scalar fields by Extreme Mass Ratio Inspirals with a Kerr black hole
• The no-hair theorem and black hole shadows
• Scalar field perturbation around a rotating hairy black hole: quasinormal modes, quasibound states and superradiant instability
• Testing the Speed of Gravity with Black Hole Ringdown
• Linear vs. nonlinear modeling of black hole ringdowns
• Bounds on the Horndeski Gauge-Gravity Coupling
• Perturbations of massless external fields in Horndeski hairy black hole
• Extreme Mass Ratio Inspirals with Scalar Hair
• Numerical computation of quasinormal modes in the first-order approach to black hole perturbations in modified gravity
• Gravitational ringdown in the Minimal Theory of Massive Gravity

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