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

Abstract

AbstractWe 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 $$x_{ps}$$ x ps , the critical impact parameter $$u_{ps}$$ u ps , the deflection angle $$\alpha _D(\theta )$$ α D ( θ ) and angular position $$\theta _{\infty }$$ θ ∞ also increases. Meanwhile, the angular separation s decreases, and relative magnitude $$r_{mag}$$ r mag 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 $$\theta _{\infty }$$ θ ∞ $$\in $$ ∈ (16.4, 39.8) $$\upmu $$ μ as, while for M87* $$\in $$ ∈ (12.33, 29.9) $$\upmu $$ μ as. The angular separation s, for SMBHs Sgr A* and M87*, differs significantly, with values ranging $$\in $$ ∈ (0.008–0.376) $$\upmu $$ μ as for Sgr A* and $$\in $$ ∈ (0.006–0.282) $$\upmu $$ μ as for M87*. The deviations of the lensing observables $$\Delta \theta _{\infty }$$ Δ θ ∞ and $$\Delta s$$ Δ s for LMRBH ($$a=0.80,l=2.0$$ a = 0.80 , l = 2.0 ) from Kerr black holes can reach up to $$10.22\,\upmu $$ 10.22 μ as and $$0.241~\upmu $$ 0.241 μ as for Sgr A*, and $$7.683~\upmu $$ 7.683 μ as and $$0.181~\upmu $$ 0.181 μ as for M87*. The relative magnitude $$r_{mag}$$ r mag $$\in $$ ∈ (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 $$1 \sigma $$ 1 σ 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 $$\theta _{sh}$$ θ sh 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*.