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

Vittorio De Falco, Emmanuele Battista, Davide Usseglio, Salvatore Capozziello

Abstract

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.

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

Abstract

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.
Paper Structure (21 sections, 50 equations, 3 figures, 1 table)

This paper contains 21 sections, 50 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Einstein-Cartan model
  4. Gravitational waveform and fluxes
  5. Binary systems
  6. Back-reaction model in Einstein-Cartan theory: a heuristic approach
  7. Quasi-elliptic orbit
  8. Damour-Deruelle parametrization
  9. Source energy and angular momentum
  10. Time average of energy and angular momentum fluxes
  11. Differential equations for $a_R(t)$ and $e_R(t)$
  12. Orbit and gravitational waveform
  13. Quasi-circular orbit
  14. Orbit and gravitational waveform
  15. Orbital frequency and phase
  16. ...and 6 more sections

Figures (3)

  • Figure 1: Plots related to the event GW150914, whose parameters can be read off from Table \ref{['tab:Table1']}. Panel (a).$R$ vs. $t$ for the quasi-elliptic dynamics and with $700$ s $\leq t \leq T_{\rm circ}$. The blue line is at $R_{\rm ISCO}$ and the dashed one at $a(T_{\rm circ})$. Panel (b).$R$ vs. $t$ for quasi-circular orbits, where the blue, red, and purple lines are located at $R_{\rm ISCO}$, $R_{\rm coal}$, and $R=0$, respectively. Panel (c). Orbits of the two objects starting at $t=800$ s, where continuous and dotted lines indicate the quasi-elliptic and the quasi-circular case, respectively. The black (blue) line follows body 1 (2). Panel (d). Plus polarization waveform $h_+(t)$ plotted for $600$ s $\leq t \leq T_{\rm coal}$, the black (red) line referring to the quasi-elliptic (quasi-circular) motion.
  • Figure 2: Comparison between the precession and GW emission timescales in terms of the semi-major axis and eccentricity.
  • Figure 3: Left panel. Plot of $\mathcal{E}$ in terms of $m_1$ and $m_2$ (with $m_1\geq m_2$). Right panel.$\mathcal{E}$ as a function of $M$, with $m_1=\frac{2}{3}M$ and $m_2=\frac{1}{3}M$.