  Explaining the late time acceleration is one of the most challenging tasks
for theoretical physicists today. Infra-red modification of Einstein's general
theory of relativity (GR) is a possible route to model late time acceleration.
In this regard, vector-tensor theory as a part of gravitational interactions on
large cosmological scales, has been proposed recently. This involves
generalization of massive Proca lagrangian in curved space time. Black hole
solutions in such theories have also been constructed. In this paper, we study
different astrophysical signatures of such black holes. We first study the
strong lensing and time delay effect of such static spherically symmetric black
hole solutions, in particular for the case of gravitational lensing of the star
S2 by Sagittarius A* at the centre of Milky Way. We also construct the rotating
black hole solution from this static spherically symmetric solution in Proca
theories using the Newman-Janis algorithm and subsequently study lensing, time
delay and black hole shadow effect in this rotating black hole space time. We
discuss the possibility of detecting Proca hair in future observations.
