Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order

Area of Science:

• Gravitational physics
• High-energy particle theory
• Computational astrophysics

Background:

• Classical scattering amplitudes are crucial for understanding gravitational interactions.
• The post-Minkowskian expansion provides a framework for strong gravity regimes.
• Modern amplitude techniques offer new computational tools for gravity.

Purpose of the Study:

• To compute the classical scattering amplitude for massive scalars interacting gravitationally.
• To derive the conservative Hamiltonian for compact spinless binaries.
• To extend the post-Minkowskian expansion to the third order.

Main Methods:

• Utilizing the modern amplitudes program, including generalized unitarity.
• Employing the double-copy construction to relate gravity to gauge theories.
• Applying effective field theory methods for integration and matching.

Main Results:

• The scattering amplitude at third post-Minkowskian order was successfully computed.
• The conservative Hamiltonian for compact spinless binaries was extracted.
• Derived results show agreement with fourth post-Newtonian order and probe limit calculations.

Conclusions:

• The study successfully computed gravitational scattering amplitudes and derived Hamiltonians using advanced amplitude techniques.
• The findings are consistent with existing theoretical frameworks, validating the methods used.
• This work provides a foundation for further investigations into strong-gravity phenomena.