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

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

6 May 2024 | Christoph Dlapa, Gregor Kälin, Zhengwen Liu, Rafael A. Porto
This paper presents the derivation of the universal (non-spinning) local-in-time conservative dynamics at fourth Post-Minkowskian order, specifically at \(\mathcal{O}(G^4)\). The authors compute the nonlocal-in-time contribution to the deflection angle and remove it from the total conservative value to obtain the local-in-time counterpart. They reconstruct the local radial action, center-of-mass momentum, and Hamiltonian, along with the exact logarithmic-dependent parts, all applicable to generic orbits. The results are valid for both hyperbolic and elliptic-like motion, with the nonlocal terms for elliptic-like motion incorporated up to sixth Post-Newtonian order. The combined Hamiltonian matches the state-of-the-art in Post-Newtonian theory within the overlap region, providing the most accurate description of gravitationally-bound binaries using scattering data. This work is crucial for improving the accuracy of waveform models for gravitational waves from compact binary systems.This paper presents the derivation of the universal (non-spinning) local-in-time conservative dynamics at fourth Post-Minkowskian order, specifically at \(\mathcal{O}(G^4)\). The authors compute the nonlocal-in-time contribution to the deflection angle and remove it from the total conservative value to obtain the local-in-time counterpart. They reconstruct the local radial action, center-of-mass momentum, and Hamiltonian, along with the exact logarithmic-dependent parts, all applicable to generic orbits. The results are valid for both hyperbolic and elliptic-like motion, with the nonlocal terms for elliptic-like motion incorporated up to sixth Post-Newtonian order. The combined Hamiltonian matches the state-of-the-art in Post-Newtonian theory within the overlap region, providing the most accurate description of gravitationally-bound binaries using scattering data. This work is crucial for improving the accuracy of waveform models for gravitational waves from compact binary systems.
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