# Testing General Relativity with X-ray reflection spectroscopy: The Konoplya-Rezzolla-Zhidenko parametrization

## TL;DR

This paper explores the use of X-ray reflection spectroscopy to test deviations from the Kerr black hole model in general relativity, implementing a parametrized non-Kerr metric and deriving observational constraints.

## Contribution

It introduces the implementation of the Konoplya-Rezzolla-Zhidenko black hole metric in the extsc{relxill extunderscore nk} framework for testing non-Kerr black holes with X-ray data.

## Key findings

- First X-ray constraints on deformation parameters of the non-Kerr metric.
- Analysis of how strong-field parameters affect observable spectra.
- Comparison of X-ray constraints with gravitational wave and black hole imaging results.

## 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 \& Zhidenko (Phys. Rev. D93, 064015, 2016) form an important class of non-Kerr black holes. We implement this class of black hole metrics in \textsc{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 \textit{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.