Testing non-circular black hole spacetime with X-ray reflection

TL;DR

This paper develops a method to test non-circular black hole spacetimes using X-ray reflection spectroscopy and applies it to real data, finding results consistent with the Kerr black hole model.

Contribution

It introduces a relativistic ray-tracing model for non-circular metrics and demonstrates its application to observational data, enabling tests of alternative black hole geometries.

Findings

Current data are consistent with Kerr black holes.

The model can constrain deviations from circularity.

High spin and inclination are inferred for the source.

Abstract

X-ray reflection spectroscopy is a powerful tool for testing the Kerr hypothesis and probing the strong gravity regime around accreting black holes. Most tests of General Relativity (GR) assume that the spacetime around a black hole is circular, meaning the metric possesses a specific symmetry structure common to the Kerr solution. However, deviations from circularity are predicted by various modified gravity theories and non-vacuum General Relativity solutions. In this work, we test a specific non-circular metric constructed based on a locality principle, where the deviation from the Kerr spacetime is driven by the local spacetime curvature. To accurately model the reflection spectrum in this background, we implement a relativistic ray-tracing code in horizon-penetrating (ingoing Kerr) coordinates, which are favored for their ability to avoid introducing curvature singularities at the horizon in non-circular spacetimes. We apply this model to the high-quality \textit{NuSTAR} spectrum of the Galactic black hole binary EXO 1846--031. Our spectral analysis reveals a source with a high inclination angle ($\iota \approx 76^{\circ}$) and a near-extremal spin parameter ($a_* \approx 0.98$). While we identify a global minimum in the parameter space suggesting a non-zero deformation ($\ell_{\mathrm{NP}} \approx 0.12$), the 99\% confidence interval fully encompasses the Kerr limit ($\ell_{\mathrm{NP}}=0$). We conclude that the current X-ray reflection data for EXO 1846--031 are consistent with the Kerr hypothesis. This work demonstrates the feasibility of using X-ray reflection spectroscopy to constrain non-circular metrics and establishes a framework for future tests.