Black Hole Gravitational Phenomena in Higher-Order Curvature–Scalar Gravity

This work aims to explore the gravitational consequences of a recently proposed black hole solution previously introduced, which incorporates quantum gravitational corrections of General Relativity. We initiate our analyses by taking into account the horizon structure, focusing on both the event and Cauchy horizons. Subsequently, we examine the quasinormal modes by considering all types of perturbations—scalar, vector, tensor, and spinorial. To strengthen these results, we also compute the time domain for each perturbation. Next, we turn to the study of optical properties of the black hole. In particular, we investigate null geodesics, the photon sphere and its stability, and the corresponding black hole shadows. Following this, we analyze gravitational lensing phenomena in two regimes: the weak-field limit, utilizing the Gauss–Bonnet theorem, and the strong deflection limit, employing Tsukamoto’s approach. In addition, we address the lensing observables with Event Horizon Telescope (EHT) data for SgrA* and M87*. Finally, constraints on the parameter ξ—which is introduced by higher-order curvature–scalar gravity, thereby differing from the Schwarzschild solution—are estimated using Solar System measurements such as the precession of Mercury’s orbit, gravitational light bending, and time delay (or the Shapiro effect).