Local in Time Conservative Binary Dynamics at Fourth Post-Minkowskian Order

Area of Science:

• General Relativity
• Gravitational Physics
• Astrophysical Dynamics

Background:

• Describing binary systems in generic orbits requires understanding local and nonlocal effects in time.
• Previous work established conservative dynamics but lacked a complete local-in-time description.

Purpose of the Study:

• To derive the universal local-in-time conservative dynamics for nonspinning binary systems at fourth post-Minkowskian order (O(G^4)).
• To incorporate nonlocal-in-time effects and reconstruct key dynamical quantities for generic orbits.

Main Methods:

• Computed the nonlocal-in-time contribution to the deflection angle.
• Removed nonlocal effects from the full conservative value to isolate local dynamics.
• Reconstructed radial action, center-of-mass momentum, and Hamiltonian for generic orbits.

Main Results:

• Derived the universal nonspinning local-in-time conservative dynamics at O(G^4).
• Successfully incorporated nonlocal terms for ellipticlike motion up to sixth post-Newtonian order.
• Achieved excellent agreement with the post-Newtonian state-of-the-art in the overlapping regime.

Conclusions:

• The derived dynamics provide the most accurate description of gravitationally bound binaries using scattering data to date.
• These results are readily applicable to gravitational waveform modeling for binary systems.