Scattering Amplitudes and Conservative Binary Dynamics at O(G^{5}) without Self-Force Truncation

Area of Science:

• Gravitational Physics
• General Relativity
• Computational Astrophysics

Background:

• Accurate modeling of gravitational interactions is crucial for understanding compact object mergers.
• Previous calculations were limited in precision and did not fully incorporate self-force effects.

Purpose of the Study:

• To compute potential-graviton contributions to the conservative radial action and scattering angle for two nonspinning bodies.
• To achieve accuracy through fifth order in Newton's constant, including second-order self-force effects.
• To develop novel computational techniques for high-order calculations in general relativity.

Main Methods:

• Utilizing the scattering-amplitude framework, combining double-copy, effective field theory, and multiloop integration.
• Employing integration by parts and differential equations for multiloop calculations.
• Developing improved integration-by-parts algorithms to overcome computational bottlenecks.

Main Results:

• The complete potential-graviton contributions to the conservative radial action and scattering angle were computed.
• A post-Minkowskian amplitude was derived as a series expansion.
• A closed-form analytic expression was obtained for the first self-force sector, involving polylogarithmic functions.

Conclusions:

• The study provides a significant advancement in the precision of gravitational wave calculations.
• The developed computational methods enable tractable high-order calculations in general relativity.
• Nontrivial cancellations were observed in the second self-force sector, offering insights into complex gravitational phenomena.