2022ApJ...938..104K

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 ≈ 0.226 corresponds to an extremal black hole with degenerate horizons. Interestingly, the spacetime admits a photon sphere for 0 < b ≤ b_P ≈ 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 α_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 θ_∞ 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 ∼8.8809 and ∼12,701.8 minutes, respectively, at b = 0.2, deviating from Schwarzschild black holes by ∼2.615 and ∼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 θ_sh of Sgr A* and M87* within the 1σ 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.