Probing Starobinsky-Bel-Robinson gravity: Gravitational lensing, thermodynamics, and orbital dynamics

This paper investigates the implications of Starobinsky-Bel-Robinson (SBR) gravity on gravitational lensing and geodesic dynamics around black holes. By incorporating higher-order curvature corrections through the Bel-Robinson tensor, we derive a modified spherically symmetric metric with a dimensionless coupling parameter β that significantly alters black hole properties. Applying the Gauss-Bonnet theorem, we calculate the weak deflection angle of light in both vacuum and plasma environments, demonstrating that increasing β enhances the bending of light, particularly in high-curvature regions. Our analysis reveals frequency-dependent effects in plasma media that could provide observational signatures distinguishing SBR gravity from general relativity. Additionally, we examine the stability of geodesic orbits using Lyapunov exponents and explore the concept of effective surface gravity through inaffinity analysis, showing how higher-curvature terms influence the behavior of particle trajectories near black holes. We also derive modified expressions for Hawking temperature, revealing how quantum corrections in SBR gravity affect black hole thermodynamics.