Scattering Amplitudes and Conservative Binary Dynamics at O(G^{4}).

Area of Science:

• * Gravitational physics
• * Theoretical astrophysics
• * High-energy particle physics

Background:

• * Understanding the dynamics of binary systems is crucial for interpreting gravitational wave signals.
• * Previous calculations of conservative binary dynamics were limited to lower post-Minkowskian orders.
• * Modern scattering amplitude techniques offer new avenues for tackling complex gravitational problems.

Purpose of the Study:

• * To compute the conservative dynamics of binary systems in general relativity at fourth post-Minkowskian order (O(G^4)).
• * To derive the radial action and Hamiltonian from scattering amplitudes.
• * To determine the energy loss due to gravitational wave radiation at third post-Minkowskian order (O(G^3)).

Main Methods:

• * Employing advanced scattering amplitude techniques, including generalized unitarity and the double copy.
• * Utilizing effective field theory and sophisticated multiloop integration methods.
• * Deriving the radial action and Hamiltonian directly from the calculated classical amplitude.

Main Results:

• * Obtained potential contributions to conservative binary dynamics at O(G^4).
• * The resulting classical amplitude involves polylogarithms and elliptic integrals.
• * Derived results align with existing lower-order post-Newtonian (PN) calculations and the probe limit.
• * Calculated the post-Minkowskian energy loss at O(G^3) via the tail effect.

Conclusions:

• * The scattering amplitude approach successfully extends conservative binary dynamics calculations to higher post-Minkowskian orders.
• * The derived Hamiltonian and energy loss provide crucial inputs for accurate gravitational wave modeling.
• * This work demonstrates the power of modern amplitude methods in addressing fundamental problems in general relativity.