Testing general relativity with x-ray reflection spectroscopy: The Konoplya-Rezzolla-Zhidenko parametrization

Abstract

X-ray reflection spectroscopy is a promising technique for testing general relativity in the strong-field regime as it can be used to test the Kerr black hole hypothesis. In this context, the parametrically deformed black hole metrics proposed by Konoplya, Rezzolla, and Zhidenko [Phys. Rev. D 93, 064015 (2016)] form an important class of non-Kerr black holes. We implement this class of black hole metrics in RELXILL_NK, which is a framework we have developed for testing for non-Kerr black holes using x-ray reflection spectroscopy. We perform a qualitative analysis of the effect of the leading order strong-field deformation parameters on typical observables like the innermost stable circular orbits and the reflection spectra. We also present the first x-ray constraints on some of the deformation parameters of this metric, using Suzaku data from the supermassive black hole in Ark 564, and compare them with those obtained (or expected) from other observational techniques like gravitational waves and black hole imaging.

Towards Precision Measurements of Accreting Black Holes Using X-Ray Reflection Spectroscopy

“…All spectra are calculated assuming the following values of the model parameters: a * = 0.99, i = 30 • , log ξ = 3.1, A Fe = 5, Γ = 2, E cut = 300 keV, q = 6, and R in = R ISCO . Figure readapted from Nampalliwar et al (2020).…”

“…Fig.21Impact of the deformation parameters δ i (i = 1, 2, ... 6) defined inNampalliwar et al (2020) for the parametric BH spacetime proposed inKonoplya et al (2016). The δ i = 0 case corresponds to the Kerr solution and in every panel only one of the deformation parameters is allowed to be non-vanishing.…”

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

“…The KRZ metric reduces to the Kerr solution when all the parameters are identically set to zero 1 . The deformation parameters have their physical interpretations which could help mapping the metric to other theories of gravity; they are listed as follows [6,27]:…”

“…Bounds can be set on the deformation parameters {δ i } to avoid certain pathologies in the spacetime outside of the horizon. These can be avoided by following certain conditions: the metric determinant must be always negative, the metric coefficient g φφ must be greater than zero, and N 2 must be non-vanishing [27]. Implying these conditions give the following bounds on the KRZ deformation 1 The metric does not reduce to the Kerr solution in the expression provided in Ref.…”

Constraining the Konoplya-Rezzolla-Zhidenko deformation parameters II: limits from stellar-mass black hole X-ray data

“…In this work, we continue the study of the Konoplya-Rezolla-Zhidenko (KRZ) parameterized BH metric [25], earlier done with the supermassive BHs in Seyfert-1 galaxies Ark 564 in Ref. [26] (wherein we also analyze the effect of the deformation parameters on the reflection spectrum and present the implementation of the KRZ metric in the data analysis framework) and MCG-06-30-15 in Ref. [27] (hereafter Paper I).…”