Analytical study of fundamental oscillation frequencies around black holes in nonlocal gravity

Abstract In this study, we investigate the dynamics of test particles in the spacetime of a static, spherically symmetric black hole (BH) illustrated within nonlocal gravity models. After presenting the BH geometries and horizon structures, we examine the motion of particles by analyzing the effective potential, innermost stable circular orbits, and corresponding effective force. We then extend the study to small perturbations of circular orbits, exploring harmonic oscillations characterized by frequencies measured by both local and distant observers, as well as the periastron precession effects. Particular attention is given to the interplay between the nonlocal gravity corrections and the stability properties of geodesics. We analyze the center-of-mass energy of colliding particles near the event horizon and show the influence of BH parameters on energy extraction processes. The results show the mechanism of influnece of nonlocal modifications of gravity on the standard predictions of the BH structure, orbital stability, and high-energy particle dynamics, with possible implications for astrophysical observations and theoretical models of strong gravity. This study examines the differences between the inverse electrodynamics of BHs and the Schwarzschild BH configuration, demonstrating the influnece of additional parameters on the dynamics and stability of test particles.