A new framework projects perturbations onto resonant frequencies via Hansen coefficients to produce efficient coupled ODEs for orbital elements in GW-driven relativistic binaries, demonstrated on tidal fields and accretion disks.
Binary black-hole problem a t the third post-Newtonian approximation in the orbital motion: Static part
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abstract
Post-Newtonian expansions of the Brill-Lindquist and Misner-Lindquist solutions of the time-symmetric two-black-hole initial value problem are derived. The static Hamiltonians related to the expanded solutions, after identifying the bare masses in both solutions, are found to differ from each other at the third post-Newtonian approximation. By shifting the position variables of the black holes the post-Newtonian expansions of the three metrics can be made to coincide up to the fifth post-Newtonian order resulting in identical static Hamiltonians up the third post-Newtonian approximation. The calculations shed light on previously performed binary point-mass calculations at the third post-Newtonian approximation.
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Experiments confirm general relativity to high precision in weak-field and strong-field regimes, with gravitational wave damping matching predictions to better than 0.5 percent.
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Dynamics of Relativistic Binaries in Structured and Stochastic Environments: A Lagrange-Fourier-Hansen Framework
A new framework projects perturbations onto resonant frequencies via Hansen coefficients to produce efficient coupled ODEs for orbital elements in GW-driven relativistic binaries, demonstrated on tidal fields and accretion disks.
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The Confrontation between General Relativity and Experiment
Experiments confirm general relativity to high precision in weak-field and strong-field regimes, with gravitational wave damping matching predictions to better than 0.5 percent.