Homoclinic Orbit of Kerr Black Holes

Objective: This study investigates the effective potential and homoclinic orbit near the Kerr metric system of black holes. It also examines the graphical relationship between effective potential and radial momentum with distance from black holes. Methods: The motion of a test particle near the Kerr metric has been analyzed using the Euler Lagrangian and action-angle variable methods. The graphical analysis in this study was performed with Mathematica software. Findings: An expression for effective potential and radial momentum has been evaluated. It has been shown that homoclinic orbits exist near the Kerr metric. This study presents a graphical analysis of the effective potential of test particles in Kerr metric black holes with different polar angle and spin. Homoclinic orbits are visually represented in this paper with the help of graphical analysis. Novelty: A physical interpretation of the effective potential and geodesic motion near Kerr metric black holes has been obtained. These results provide a valuable tool for detecting chaos in the Kerr metric of black holes. In this paper, we have shown the changes in the motion of a particle when it comes near the horizon of Kerr black holes. Indicators of chaos can give an insight into understanding the black hole phenomena. Graphical analysis offers a visual understanding of the motion of test particles near the Kerr metric geometry of Black holes. Keywords: Black holes, Kerr Metric, Melnikov method, Chaos, Effective Potential, Homoclinic Orbit