Vol. 7, Issue 2, Part C (2025)

Black holes represent the most extreme manifestations of gravity in our universe. The interactions presented by Black holes provide the profound insights into the nature of spacetime. Among these phenomena the black hole scattering is of increasing relevance due to its connection with gravitational-wave astronomy in the post-Minkowskian expansions and high-precision theoretical physics. Here we have presented a comprehensive study of the characteristic features of black hole scattering in the high-precision regime. Recent advances have elevated the predictive power of theory to the fifth post-Minkowskian order, revealing unexpected mathematical structures. These discoveries not only improve waveform modeling for gravitational wave observatories but also uncover new connections between general relativity, quantum field theory, and algebraic geometry. The spin effect sand finite mass-ratio corrections have also been discussed in this study.