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

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.

arXiv comment13 pages, 2 figures, accepted for pubblication on Phys. Rev. D

References in corpus (20)

• Modified Gravity and Cosmology
• A Massive Pulsar in a Compact Relativistic Binary
• Extended Theories of Gravity
• Coalescing binary systems of compact objects to (post)$^{5/2}-Newtonian order. V. Spin Effects
• Timing Measurements of the Relativistic Binary Pulsar PSR B1913+16
• Spin effects in the inspiral of coalescing compact binaries
• Modified teleparallel theories of gravity
• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Higher-order spin effects in the dynamics of compact binaries II. Radiation field
• Gravitational waves from inspiraling compact binaries: The quadrupole-moment term
• Comparing Equivalent Gravities: common features and differences
• Gravitational waves at the first post-Newtonian order with the Weyssenhoff fluid in Einstein-Cartan theory
• Upgraded Giant Metrewave Radio Telescope timing of NGC 1851A: a possible millisecond pulsar-neutron star system
• Einstein-Cartan Cosmologies
• First post-Newtonian $N$-body problem in Einstein-Cartan theory with the Weyssenhoff fluid: Lagrangian and first integrals
• First post-Newtonian $N$-body problem in Einstein-Cartan theory with the Weyssenhoff fluid: equations of motion
• PSR~J1910$-$5959A: A rare gravitational laboratory for testing white dwarf models
• Understanding and improving the timing of PSR J0737-3039B
• Relativistic cosmology and intrinsic spin of matter: Results and theorems in Einstein-Cartan theory
• Analytical coordinate time at first post-Newtonian order

Cited by in corpus (21)

• Radiative losses and radiation-reaction effects at the first post-Newtonian order in Einstein-Cartan theory
• Large fluctuations and Primordial Black Holes
• Null energy condition violation during inflation and pulsar timing array observations
• Obviating PBH overproduction for SIGWs generated by Pulsar Timing Arrays in loop corrected EFT of bounce
• Charting the Nanohertz Gravitational Wave Sky with Pulsar Timing Arrays
• Torsion at different scales: from materials to the Universe
• Gravitational Radiation from Eccentric Binary Black Hole System in Dynamical Chern-Simons Gravity
• Negative non-Gaussianity as a salvager for PBHs with PTAs in bounce
• Gravitational waves for eccentric extreme mass ratio inspirals of self-dual spacetime
• Implications of Pulsar Timing Array Results for High Frequency Gravitational Waves
• Prospects of constraining on the polarizations of gravitational waves from binary black holes using space- and ground-based detectors
• Motions of spinning particles and chaos bound in Reissner-Nordström spacetime
• Signatures of modified gravity from the gravitational Aharonov-Bohm effect
• Effects of gravitational waves on electromagnetic fields
• Evolution of the early universe in Einstein-Cartan theory
• Gravitational waves from equatorially eccentric extreme mass ratio inspirals around swirling Kerr black holes
• Compact binary system dynamics at the second post-Newtonian order: analytical formula of the coordinate time for eccentric and circular orbits
• Post-Newtonian Dynamics of Radiating Charges: Canonical Formulation and Binary Inspiral Laws
• Cosmology in the De Donder-Weyl Formulation of Einstein-Cartan Gravity
• Propagation and emission of gravitational waves in the weak-field limit within the Palatini formalism
• One-Dimensional Primordial Gravitational Waves In Pure Quadratic Gravity