Strong Gravitational Lensing by Static Black Holes in Effective Quantum Gravity

Abstract

We investigate strong gravitational lensing by two static black hole models (Model-1 and Model-2) within the Effective Quantum Gravity (EQG) framework, characterized by mass $M$ and parameter $\hat{I}\P$. For $\hat{I}\P =0$, they reduce to the Schwarzschild solution, and depending on the parameters, they describe black holes with an event and Cauchy horizon (Model-1), a single horizon (Model-2), or no horizons. Using SMBHs Sgr A* and M87* as lenses and integrating theoretical predictions with recent EHT data, we identify significant differences in lensing signatures due to quantum corrections. For Model-1, the deviations of the lensing observables: $|\hat{I}´\hat{I}{¸}_{\infty }|$ of black holes in EQG from Schwarzschild black hole, for SMBHs Sgr A* and M87, can reach as much as $1.75\hat{I}¼$as and $1.32\hat{I}¼$as, while $|\hat{I}´s|$ is about $30.12$~nas for Sgr A* and $22.63$~nas for M87*. The flux ratio of the first image to all subsequent packed images indicates that EQG black hole images are brighter than their Schwarzschild counterparts, with a deviation in the brightness ratio $|\hat{I}´r_{mag}|$ reaching up to 2.02. The time delays between the second and first images, denoted $|\hat{I}´T_{2,1}|$, exhibit substantial deviations from the GR counterpart, reaching up to 1.53 min for Sgr A* and 1159.9 min for M87*. The EHT constraints on $\hat{I}{¸}_{sh}$ of Sgr A* and M87* within the $1\ddot{I}ƒ$ region limit the parameters $\hat{I}\P$. Our analysis concludes that EQG black holes are consistent with the EHT observations within this finite space.

The paper is submitted to EPJC on 2024-10-03