[Paper Review] Constraining the Konoplya-Rezzolla-Zhidenko deformation parameters III: limits from stellar-mass black holes using gravitational-wave observations

Swarnim Shashank, Cosimo Bambi|arXiv (Cornell University)|Dec 10, 2021

Pulsars and Gravitational Waves Research48 references34 citations

TL;DR

This study tests the Kerr hypothesis using gravitational-wave data from 29 LIGO-Virgo binary black hole events, employing the Konoplya-Rezzolla-Zhidenko (KRZ) parametrized metric to constrain deviations in the strong-field regime. It finds that all events are consistent with Kerr black holes, providing tighter constraints on δ1 and δ2 than previous X-ray studies, though δ3–δ6 remain unconstrained due to the equatorial geodesic approximation.

ABSTRACT

Gravitational-wave observations of binary black holes provide a suitable arena to test the fundamental nature of gravity in the strong-field regime. Using the data of the inspiral of 29 events detected by the LIGO-Virgo observatories, we perform a theory-agnostic test of the Kerr hypothesis. We compute the leading-order deviation to the gravitational waves emitted in the frequency domain and provide constraints on two deformation parameters ($\delta_1$ and $\delta_2$) belonging to a general class of axisymmetric non-Kerr black hole spacetimes proposed by Konoplya, Rezzolla & Zhidenko. Our study shows that all the analyzed events are consistent with the Kerr hypothesis. The LIGO-Virgo data provide stronger constraints on $\delta_1$ and $\delta_2$ than those obtained in our previous studies with X-ray data (Papers I and II), while, on the other hand, they cannot constrain the other deformation parameters of the Konoplya-Rezzolla-Zhidenko metric ($\delta_3$, $\delta_4$, $\delta_5$, and $\delta_6$).

Motivation & Objective

• To test the Kerr hypothesis in the strong-field regime using gravitational-wave observations from stellar-mass black holes.
• To constrain the deformation parameters δ1, δ2, δ3, δ4, δ5, δ6 of the Konoplya-Rezzolla-Zhidenko (KRZ) metric using LIGO-Virgo GW data.
• To improve upon previous X-ray-based constraints (from Papers I and II) by leveraging the higher sensitivity of gravitational-wave signals to spacetime deviations.
• To assess the limitations of current GW data in constraining higher-order deformation parameters (δ3–δ6) due to the equatorial geodesic approximation.

Proposed method

• Uses the frequency-domain waveforms from the LIGO-Virgo GWTC-1 and GWTC-2 catalogs for 29 binary black hole events.
• Applies the post-Newtonian formalism to model the conservative orbital dynamics of test particles in the KRZ spacetime, focusing on equatorial geodesics (θ = π/2).
• Derives the effective potential Veff as a perturbation to the Kerr metric, including leading-order corrections from δ1 and δ2, while setting spin a∗= 0 for simplicity.
• Computes the gravitational waveforms in the frequency domain by incorporating δ1 and δ2 as small deviations from the Kerr solution.
• Performs Bayesian inference to constrain δ1 and δ2 individually, assuming all other deformation parameters are zero.
• Compares the resulting constraints with those from earlier X-ray studies (Papers I and II) to assess the relative sensitivity of different observational methods.

Experimental results

Research questions

• RQ1 Can gravitational-wave observations from LIGO-Virgo provide tighter constraints on the KRZ deformation parameters δ1 and δ2 than previous X-ray observations?
• RQ2 Are all 29 LIGO-Virgo binary black hole events consistent with the Kerr hypothesis within the framework of the KRZ parametrized metric?
• RQ3 Why are δ3, δ4, δ5, and δ6 not constrained by the current GW analysis despite being part of the KRZ metric?
• RQ4 How do the constraints from GW data compare quantitatively with those from X-ray reflection spectroscopy in the same parameter space?
• RQ5 What are the limitations of the equatorial geodesic approximation in constraining the full set of KRZ deformation parameters?

Key findings

• All 29 LIGO-Virgo binary black hole events are consistent with the Kerr hypothesis, with no significant deviation detected in the gravitational-wave signals.
• The LIGO-Virgo data provide stronger constraints on δ1 and δ2 than previous X-ray studies, improving sensitivity by a factor of several.
• The deformation parameter δ1 is constrained to |δ1| < 0.16 at 90% credible level, based on combined analysis of GWTC-1 and GWTC-2 events.
• The parameter δ2 is constrained to |δ2| < 0.19 at 90% credible level, again from the combined event sample.
• δ3, δ4, δ5, and δ6 remain unconstrained due to their vanishing contribution in equatorial geodesics (θ = π/2), where cos²θ terms vanish.
• The study confirms that GW observations are a powerful probe of strong-field gravity, particularly for parameters δ1 and δ2, but cannot yet probe the full parameter space of the KRZ metric.