Distinguishing a Slowly Accelerating Black Hole by Differential Time
  Delays of Images
  Accelerating supermassive black holes, connected to cosmic strings, could
contribute to structure formation and get captured by galaxies if their
velocities are small. This would mean that the acceleration of these black
holes is small too. Such a slow acceleration has no significant effect on the
shadow of such supermassive black holes. We also show that, for slowly
accelerating black holes, the angular position of images in the gravitational
lensing effects do not change significantly. We propose a method to observe the
acceleration of these black holes through the gravitational lensing. The method
is based on the observation that differential time delays associated with the
images are substantially different with respect to the case of non-accelerating
black holes. This is in contrast with when the theory governing the strong
gravitational field around the black hole is different from general relativity,
where not only the differential time delays but the angular position of images
would be different. We conclude that, if the observed angular position of
images are compatible with the prediction of general relativity, a possible
deviation in the differential time delays between the observed values and those
predicted by general relativity, could be due to the acceleration of the black
hole.
