Testing Strong Gravitational Lensing Effects of Supermassive Compact Objects with Regular Spacetimes

We compare and contrast gravitational lensing, in the strong field limit, by the photon sphere in spherically symmetric regular electrically charged (REC) black holes (0 < b <= b ( E )) and with those by corresponding REC no-horizon spacetimes (b > b ( E )). Here, b is an additional parameter due to the charge and the value b = b ( E ) approximate to 0.226 corresponds to an extremal black hole with degenerate horizons. Interestingly, the spacetime admits a photon sphere for 0 < b <= b ( P ) approximate to 0.247 and an anti-photon sphere only for b ( E ) < b <= b ( P ). With no-horizon spacetime, images by lensing from the inside of the photon sphere (u < u (ps)) can also appear. Interestingly, for the case of u < u (ps) the deflection angle alpha ( D ) increases with u. We analyze the lensing observables by modeling compact objects Sgr A*, M87*, NGC 4649, and NGC 1332 as black holes and no-horizon spacetimes. The angular position theta (infinity) and photon sphere radius x (ps) decrease with increasing parameter b. Our findings suggest that the angular separations (s) and magnification (r) of relativistic images inside the photon sphere may be higher than those outside. Moreover, the time delay for Sgr A* and M87* can reach similar to 8.8809 and similar to 12,701.8 minutes, respectively, at b = 0.2, deviating from Schwarzschild black holes by similar to 2.615 and similar to 4677 minutes. These deviations are insignificant for Sgr A* because it is too small, but they are sufficient for astronomical observation of M87* and some other black holes. With EHT bounds on the theta (sh) of Sgr A* and M87* within the 1 sigma region, placing bounds on the parameter b, our analysis concludes that REC black holes agree with the EHT results in finite space, whereas the corresponding REC no-horizon spacetimes are completely ruled out.

Automated summary

We compare and contrast the gravitational lensing in spherically symmetric regular electrically charged (REC) black holes and the corresponding REC no-horizon spacetimes in the strong field limit. Our findings suggest that REC black holes agree with EHT results in finite space, while REC no-horizon spacetimes are completely ruled out.