Radiative losses and radiation-reaction effects at the first post-Newtonian order in Einstein–Cartan theory

Gravitational radiation-reaction phenomena occurring in the dynamics of inspiralling compact binary systems are investigated at the first post-Newtonian order beyond the quadrupole approximation in the context of Einstein–Cartan theory, where quantum spin effects are modeled via the Weyssenhoff fluid. We exploit balance equations for the energy and angular momentum to determine the binary orbital decay until the two bodies collide. Our framework deals with both quasi-elliptic and quasi-circular trajectories, which are then smoothly connected. Key observables like the laws of variation of the orbital phase and frequency characterizing the quasi-circular motion are derived analytically. We conclude our analysis with an estimation of the spin contributions at the merger, which are examined both in the time domain and the Fourier frequency space through the stationary wave approximation.