Strong gravitational lensing by loop quantum gravity motivated rotating black holes and EHT observations

We investigate gravitational lensing in the strong deflection regime by loop quantum gravity (LQG)-motivated rotating black hole (LMRBH) metrics with an additional parameter l besides mass M and rotation a. The LMRBH spacetimes are regular everywhere, asymptotically encompassing the Kerr black hole as a particular case and, depending on the parameters, describe black holes with one horizon only (BH-I), black holes with an event horizon and a Cauchy horizon (BH-II), black holes with three horizons (BH-III), or black holes with no horizons (NH) spacetime. It turns out that as the LQG parameter l increases, the unstable photon orbit radius x(ps), the critical impact parameter u(ps), the deflection angle alpha(D)(0) and angular position 0,,, also increases. Meanwhile, the angular separation s decreases, and relative magnitude rmag increases with increasing l for prograde motion but they show opposite behaviour for the retrograde motion. Using supermassive black holes (SMBH) Sgr A* and M87* as lenses, we compare the observable signatures of LMRBH with those of Kerr black holes. For Sgr A*, the angular position 0,,, is an element of (16.4, 39.8) mu as, while for M87* is an element of (12.33, 29.9) mu as. The angular separations, for SMBHs Sgr A* and M87*, differs significantly, with values ranging is an element of (0.008-0.376) mu as for Sgr A* and is an element of (0.006-0.282) mu as for M87*. The deviations of the lensing observables A0,,, and As for LMRBH (a = 0.80, l = 2.0) from Kerr black holes can reach up to 10.22 mu as and 0.241 mu as for Sgr A*, and 7.683 mu as and 0.181 mu as for M87*. The relative magnitude rmag is an element of (0.047, 1.54). We estimate the time delay between the first and second relativistic images using twenty supermassive galactic centre black holes as lenses to find, for example, the time delay for Sgr A* and M87* can reach approximately 23.26 min and 33,261.8 min, respectively. Our analysis concludes that, within the 1a region, a significant portion of the BH-I and BH-II parameter space agrees with the EHT results of M87* and Sgr A*. The possibility of LMRBH being a BH-III with three horizons has been almost ruled out, except for a small portion of parameter space, by 0sh bounds of Sgr A* and M87* measured by EHT. In contrast, NH without a horizon is completely ruled out. We discover that the EHT results of Sgr A* place more stringent limits on the parameter space of LMRBH black holes than those established by the EHT results of M87*.