Conservative Binary Dynamics with a Spinning Black Hole at O(G^{3}) from Scattering Amplitudes

Area of Science:

• Gravitational physics
• Black hole astrophysics
• High-energy particle theory

Background:

• Compact binary systems, especially those involving spinning black holes, are key sources of gravitational waves.
• Accurate theoretical modeling is crucial for interpreting gravitational wave signals and testing general relativity.

Purpose of the Study:

• To compute the conservative two-body Hamiltonian for compact binary systems with spinning black holes.
• To include spin effects up to O(G^3) and all orders in velocity.

Main Methods:

• Calculation of the classical limit of two-loop scattering amplitudes for scalar-graviton and spin-1 particle interactions.
• Application of modern scattering amplitude techniques: numerical unitarity, integration-by-parts, and method of regions.
• Matching to nonrelativistic effective field theory and application of the Kosower-Maybee-O'Connell (KMOC) formalism.

Main Results:

• Derivation of the conservative two-body Hamiltonian including linear and quadratic spin terms.
• Extraction of the conservative potential in terms of rest-frame spin vectors.
• Calculation of the impulse in the covariant spin formalism using the KMOC formalism.

Conclusions:

• The study provides a significant advancement in the theoretical description of spinning compact binary systems.
• The results are essential for precise gravitational wave data analysis and understanding extreme gravity phenomena.