Analytical results for binary dynamics at the first post-Newtonian order in Einstein-Cartan theory with the Weyssenhoff fluid

TL;DR

This paper derives analytical formulas for the dynamics of binary systems with aligned spins in Einstein-Cartan theory at the first post-Newtonian order, highlighting quantum spin effects on gravitational waveforms and fluxes.

Contribution

It provides new analytical expressions for binary system dynamics incorporating quantum spin effects within Einstein-Cartan theory at the first post-Newtonian order.

Findings

Quantum spin contributions affect energy flux and gravitational waveform during inspiral.

Derived expressions enable calculation of macroscopic angular momentum from energy flux.

Results applicable to astrophysical scenarios involving spin effects in gravitational wave emission.

Abstract

The quantum spin effects inside matter can be modeled via the Weyssenhoff fluid, which permits to unearth a formal analogy between general relativity and Einstein-Cartan theory at the first post-Newtonian order. In this framework, we provide some analytical formulas pertaining to the dynamics of binary systems having the spins aligned perpendicular to the orbital plane. We derive the expressions of the relative orbit and the coordinate time, which in turn allow to determine the gravitational waveform, and the energy and angular momentum fluxes. The potentialities of our results are presented in two astrophysical applications, where we compute: ($i$) the quantum spin contributions to the energy flux and gravitational waveform during the inspiral phase; ($ii$) the macroscopic angular momentum of one of the bodies starting from the time-averaged energy flux and the knowledge of few timing parameters.