Physical properties of black hole solutions in Einstein–Bel–Robinson gravity

In this paper, we study the different properties of static spherically symmetric black hole solutions of Einstein–Bel–Robinson gravity (EBR), a modified four-dimensional theory of gravity quartic in curvature. We look at the implications of EBR gravity on the orbit of massless and massive test bodies, derive modified expressions, and show how the higher curvature term influences the behavior of particle trajectories near black holes. Specifically, computing the innermost stable circular orbit and photon sphere, and finding them smaller than their Einstein counterparts in general relativity. Next, we obtain the deflection angle and shadow of an EBR black hole and find that both decrease compared to a non-rotating black hole in general relativity. Using the Shapiro time delay, we obtain a bound value for the coupling constant. Then, we explore the EBR black hole’s lifetime and find that it decreases to Einstein’s gravity. Quasinormal modes (QNMs) are computed using Padé averaged sixth-order WKB method, showing that increasing the coupling constant lowers the damping rate of ring-down gravitational waves (GWs). The oscillation frequency of scalar QNMs decreases with the coupling constant, whereas it increases for electromagnetic QNMs. We also provide an analytically rigorous bound on the greybody factor. We show that the coupling constant has a small effect on the greybody factor. Finally, correspondence between the greybody factor and quasinormal modes is also considered.