From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion.

Area of Science:

• Theoretical Physics
• Gravitational Physics
• Quantum Field Theory

Background:

• Calculating the classical potential for interacting particles, especially in strong gravity regimes like binary black holes, is complex.
• Existing methods often become cumbersome at higher orders of approximation.

Purpose of the Study:

• To develop a novel method for mapping on-shell scattering amplitudes to classical potentials.
• To derive analytic expressions for the classical potential of binary black hole systems.

Main Methods:

• Combining techniques from effective field theory and generalized unitarity.
• Constructing a mathematical map between scattering amplitudes and classical potentials.

Main Results:

• Analytic expressions for the binary black hole classical potential at second order in the gravitational constant and all orders in velocity.
• Exact agreement with all known results up to the fourth post-Newtonian order.

Conclusions:

• The developed methods provide a powerful and systematic way to calculate classical potentials.
• This approach offers a simplified check for future higher-order calculations in gravitational physics.
• The framework is designed to be extensible to higher orders in perturbation theory.