Shadows and strong gravitational lensing around black hole-like compact object in quadratic gravity

We investigate the astrophysical consequences of black holes in quadratic gravity, characterized by the parameters $S_0$, $S_2$, $m_0$ and $m_2$, in addition to the black hole mass M. To evaluate the physical validity of the fundamental quadratic gravity black hole solutions, we analyze their gravitational lensing properties in the strong deflection limit. Specifically, we examine the shadow cast by the quadratic gravity black hole and constrain its parameters using observational data from the $M{87}^{⁎}$ and $Sgr{A}^{⁎}$ supermassive black holes. Our analysis reveals that, within the 1σ confidence level, a significant portion of the parameter space for quadratic gravity black holes is consistent with the Event Horizon Telescope (EHT) observations of $M{87}^{⁎}$ and $Sgr{A}^{⁎}$. This suggests that these black holes are plausible candidates for describing astrophysical black holes. As an additional observational test, we perform a detailed investigation of the strong deflection limit properties of these black holes. We explore the fundamental lensing observables in detail, including the angular positions and separations of the lensed images, the relative magnifications, the radius of the outermost Einstein ring, and the relativistic time delay between images. We compare the predictions of the quadratic gravity black hole for each observable with those of the classical Schwarzschild solution using realistic astrophysical data. Our findings provide a pathway for testing quadratic gravity at the galactic and extragalactic scales, offering new insights into the observational properties of black hole solutions within this framework.