RELXILL_NK is a new reflection model developed by our group to test Einstein’s theory of general relativity with black holes. It is the extension of the RELXILL package developed by Thomas Dauser and Javier Garcia to non-Kerr spacetimes.


Einstein’s theory of general relativity has passed a large number of observational tests in weak gravitational fields, while the strong gravity regime is still largely unexplored. Astrophysical black holes are the most extreme objects that can be found in the Universe and thus an ideal laboratory for testing strong gravity.

In 4-dimensional general relativity, uncharged black holes are described by the Kerr solution and are completely specified by their mass and spin angular momentum. The spacetime metric around astrophysical black holes is thought to be well described by the Kerr solution.


The study of the reflection spectrum of accretion disks around black holes is potentially a powerful tool to probe the strong gravity region of these objects. RELXILL_NK can calculate the reflection spectrum of accretion disks in parametric black hole spacetimes. Some “deformation parameters” quantify possible deviations from the Kerr background. From the comparison of X-ray data of astrophysical black holes with the theoretical predictions of RELXILL_NK we can measure these deformation parameters and check whether they vanish, as it would be required by general relativity.


RELXILL_NK v1.3.2 (172 KB)

FITS file for a13 (523 MB)

FITS file for a22 (524 MB)

FITS files for non-relativistic and Kerr models (2.8 GB)

FITS file for lamppost profile for a13 (170 MB)

FITS file for lamppost profile for a22 (170 MB)

Scripts to unscale the deformation parameters (43 KB)

Quick user guide for RELXILL_NK v1.3.2 (193 KB)

[We will soon post even the FITS files for the deformation parameter e3 and for some deformation parameters of the Konoplya-Rezzolla-Zhidenko metric]

Please acknowledge use of this model in any publications and cite Refs. [1,2]


[1] Bambi et al., Testing the Kerr black hole hypothesis using X-ray reflection spectroscopy, Astrophys. J. 842, 76 (2017)

[2] Abdikamalov et al., Public Release of RELXILL_NK: A Relativistic Refletion Model for Testing Einstein's Gravity, Astrophys. J. 878, 91 (2019)


For questions, comments, and suggestions about RELXILL_NK, you can email us at