  Accelerating black holes, connected to cosmic strings could evolve to
supermassive black holes. However, if they are going to take part in structure
formation and resides at the center of galaxies, their acceleration should be
small. This slow acceleration does not change the shadow or image position in
gravitational lensing effect significantly. However we show that the time delay
associated to these images change significantly. 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.
