https://doi.org/10.1140/epjc/s10052-026-15867-x
Regular Article - Theoretical Physics
Testing non-circular black hole spacetime with X-ray reflection
1
Department of Physics, Center for Astronomy and Astrophysics, Fudan University, 200438, Shanghai, China
2
Institut für Astronomie und Astrophysik, Eberhard-Karls Universität Tübingen, 72076, Tübingen, Germany
3
School of Natural Sciences and Humanities, New Uzbekistan University, 100007, Tashkent, Uzbekistan
a
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Received:
8
March
2026
Accepted:
16
May
2026
Published online:
3
June
2026
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 NuSTAR spectrum of the Galactic black hole binary EXO 1846-031. Our spectral analysis reveals a source with a high inclination angle (
) and a near-extremal spin parameter (
). While we identify a global minimum in the parameter space suggesting a non-zero deformation (
), the 99% confidence interval fully encompasses the Kerr limit (
). 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.
© The Author(s) 2026
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