Probing bumblebee gravity with black hole X-ray data

Bumblebee gravity is one of the simplest gravity theories with spontaneous Lorentz symmetry breaking. Since we know a rotating black hole solution in bumblebee gravity, we can potentially test this model with the available astrophysical observations of black holes. In this work, we construct a reflection model in bumblebee gravity and we use our model to analyze the reflection features of a NuSTAR spectrum of the Galactic black hole EXO 1846-031 in order to constrain the Lorentz-violating parameter $\ell$. We find that the analysis of the reflection features in the spectrum of EXO 1846-031 cannot constrain the parameter $\ell$ because of a very strong degeneracy between the estimates of $\ell$ and of the black hole spin parameter $a_*$. Such a degeneracy may be broken by combining other observations.