Physical Properties of Black Hole Solution 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 orbit of massless and massive test bodies near a black hole, 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 by an EBR black hole and find that both decreased compared to a non-rotating black hole in general relativity. We obtain a bound value for the coupling constant using the Shapiro time delay. Then, we explore the EBR black hole's lifetime and find that it decreases to Einstein's gravity. Quasinormal modes (QNMs) are computed using Pad\'e averaged 6th 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 analytical rigorous bound of greybody factor. We show that the coupling constant has a small effect on the greybody factor. Finally, correspondence between greybody factor and quasinormal modes is also considered.