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

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 ( $$\iota \approx 76^{\circ }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ι</mml:mi> <mml:mo>≈</mml:mo> <mml:msup> <mml:mn>76</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:mrow> </mml:math> ) and a near-extremal spin parameter ( $$a_* \approx 0.98$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mmultiscripts> <mml:mi>a</mml:mi> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> <mml:mrow/> </mml:mmultiscripts> <mml:mo>≈</mml:mo> <mml:mn>0.98</mml:mn> </mml:mrow> </mml:math> ). While we identify a global minimum in the parameter space suggesting a non-zero deformation ( $$\ell _{\textrm{NP}} \approx 0.12$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mtext>NP</mml:mtext> </mml:msub> <mml:mo>≈</mml:mo> <mml:mn>0.12</mml:mn> </mml:mrow> </mml:math> ), the 99% confidence interval fully encompasses the Kerr limit ( $$\ell _{\textrm{NP}}=0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mtext>NP</mml:mtext> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ). 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.

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