Correction for the Classical Conditions for a Collision in Three-Body System Using General Relativity and Machine Learning

This paper comprehensively investigates collision conditions in three-body problems, incorporating General Relativity (GR) effects. The study analyzes the initial values of the bodies to determine the collision possibility and develops a high-accuracy machine learning model for classifying collision events. The study introduces the concept of GR-effective potential energy derived from the Einstein Field Equations and solves the equation using the Schwarzschild solution for spherically symmetric gravity fields. Additionally, a code is developed to examine collisions using the GR-effective potential energy, and a machine learning model is trained accordingly. The study provides a modified equation that accurately describes the collision condition in three-body problems, accounting for GR effects. The results have significant implications in astrophysics and contribute to advancing knowledge in understanding celestial body dynamics in collision scenarios.