Explaining the late-time acceleration is one of the most challenging tasks for theoretical physicists today. Infrared 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 a massive Proca Lagrangian in curved spacetime. 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 ${\mathrm{A}}^{*}$ 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 spacetime. We discuss the possibility of detecting the Proca hair in future observations.

• Received 29 October 2018

DOI:https://doi.org/10.1103/PhysRevD.99.024052