Strong gravitational lensing by rotating Simpson-Visser black holes

Abstract

We investigate strong field gravitational lensing by rotating Simpson-Visser black hole, which has an additional parameter (0 ≤ l/2M ≤ 1), apart from mass (M) and rotation parameter (a). A rotating Simpson-Visser metric correspond to (i) a Schwarzschild metric for l/2M = a/2M = 0 and M ≠ 0, (ii) a Kerr metric for l/2M = 0, |a/2M| < 0.5 and M ≠ 0 (iii) a rotating regular black hole metric for |a/2M| < 0.5, M ≠ 0 and l/2M in the range 0 < l/2M < 0.5 + √((0.5)2-(a/2M)2), and (iv) a traversable wormhole for a |a/2M | > 0.5 and l/2M ≠ 0. We find a decrease in the deflection angle α D and also in the ratio of the flux of the first image and all other images r mag. On the other hand, angular position θ1 increases more slowly and photon sphere radius x m decreases more quickly, but angular separation s increases more rapidly, and their behaviour is similar to that of the Kerr black hole. The formalism is applied to discuss the astrophysical consequences in the supermassive black holes NGC 4649, NGC 1332, Sgr A* and M87* and find that the rotating Simpson-Visser black holes can be quantitatively distinguished from the Kerr black hole via gravitational lensing effects. We find that the deviation of the lensing observables Δθ1 and Δs of rotating Simpson Visser black holes from Kerr black hole for 0 < l/2M < 0.6 (a/2M = 0.45), for supermassive black holes Sgr A* and M87, respectively, are in the range 0.0422–0.11658 μas and 0.031709–0.08758 μas while |Δr mag| is in the range 0.2037 – 0.95668. It is difficult to distinguish the two black holes because the departure are in \U0001d4aa(μas), which are unlikely to get resolved by the current EHT observations, and one has to wait for future observations by ngEHT can pin down the exact constraint.We also derive a two-dimensional lens equation and formula for deflection angle in the strong field limit by focusing on trajectories close to the equatorial plane.