Strong field gravitational lensing by a charged Galileon black hole

Abstract: Strong field gravitational lensings are dramatically disparate from those in the weak field by representing relativistic images due to light winds one to infinity loops around a lens before escaping. We study such a lensing caused by a charged Galileon black hole, which is expected to have possibility to evade no-hair theorem. We calculate the angular separations and time delays between different relativistic images of the charged Galileon black hole. All these observables can potentially be used to discriminate a charged Galileon black hole from others. We estimate the magnitudes of these observables for the closest supermassive black hole Sgr A*. The strong field lensing observables of the charged Galileon black hole can be close to those of a tidal Reissner-Nordstr\"{o}m black hole or those of a Reissner-Nordstr\"{o}m black hole. It will be helpful to distinguish these black holes if we can separate the outermost relativistic images and determine their angular separation, brightness difference and time delay, although it requires techniques beyond the current limit.