Testing strong gravitational lensing effects by supermassive compact objects with regular spacetimes

Abstract

We compare and contrast gravitational lensing, in the strong-field limit, by photon sphere in spherically symmetric regular electrically charged (REC) black holes ($0<b\leq b_E$) and with those by corresponding REC no-horizon spacetimes ($b>b_E$). Here, $b$ is additional parameter due to charge and the value $b=b_E \approx 0.226$ corresponds to an extremal black hole with degenerate horizons. Interestingly, the spacetime admits photon sphere for $0<b\leq b_P \approx 0.247$ and an anti-photon sphere only for $b_E < b \leq b_P$. With no-horizon spacetime, images by lensing from the inside of the photon sphere ($u<u_{ps}$) can also appear. Interestingly, for the case $u<u_{ps}$ the deflection angle $\alpha_D$ increases with $u$. We analyse the lensing observables by modelling compact objects Sgr A*, M87*, NGC4649, and NGC1332 as black holes and no-horizon spacetimes. The angular position $\theta_{\infty}$ 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 $\sim$ 8.8809 min and $\sim$ 12701.8 min, respectively, at $b = 0.2$, deviating from Schwarzschild black holes by $\sim$ 2.615 min and $\sim$ 4677 min. 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 $\theta_{sh}$ of Sgr A* and M 87*, within $1 \sigma$ region, placing bounds on the parameter $b$, our analysis concludes that the REC black holes agree with the EHT results in finite space, whereas the corresponding REC no-horizon spacetimes are completely ruled out.