We build upon recent work by Antonelli et al. [Phys. Rev. Lett. 125 (2020) 1,
011103] to obtain, within the effective-one-body (EOB) formalism, and for an
arbitrary choice of gauge, the third-subleading post-Newtonian (4.5PN)
corrections to the spin-orbit conservative dynamics of spin-aligned binaries.
This is then specialized to: (i) the well-known Damour-Jaranowski-Sch”afer
($rm DJS$) gauge, where the dependence on the angular momentum of the
gyro-gravitomagnetic functions $(G_S,G_{S_*})$ is removed and (ii) to an
alternative gauge (called anti-$rm DJS$ gauge, $overline{rm DJS}$) that is
chosen so as to precisely reproduce the Hamiltonian of a spinning test-particle
at linear order in the particle spin and keep the full dependence on the radial
and angular momentum in $(G_S,G_{S_*})$. We use these results to extend by one
perturbative order, in PN sense, the analytical knowledge of the periastron
advance. After performing a suitable factorization and resummation of
$(G_S,G_{S_*})$, the $rm DJS$ and $overline{rm DJS}$ performances are
compared via various gauge-invariant quantities at the EOB last stable circular
orbit. We eventually find some indications that the $overline{rm DJS}$ gauge
might be advantageous in the description of the inspiral dynamics of
circularized binaries.
The Future of Spin-Orbit Dynamics in Binary Systems
In recent research by Antonelli et al. [Phys. Rev. Lett. 125 (2020) 1, 011103], important progress has been made in understanding the spin-orbit dynamics of spin-aligned binaries within the effective-one-body (EOB) formalism. Building upon this work, we have further investigated the third-subleading post-Newtonian (4.5PN) corrections to the spin-orbit conservative dynamics, taking into account an arbitrary choice of gauge.
To make the analysis more tractable, we have focused on two specific gauges. The first gauge is the well-known Damour-Jaranowski-Sch”afer (DJS) gauge, where we have removed the dependence on the angular momentum of the gyro-gravitomagnetic functions $(G_S,G_{S_*})$. The second gauge, known as anti-DJS ( $overline{rm DJS}$) gauge, has been chosen to reproduce the Hamiltonian of a spinning test-particle at linear order in the particle spin and retains the full dependence on the radial and angular momentum in $(G_S,G_{S_*})$. By specializing our results to these gauges, we have been able to extend the analytical knowledge of the periastron advance by one perturbative order in the post-Newtonian sense.
In order to compare the performance of the DJS and $overline{rm DJS}$ gauges, we have conducted an analysis of various gauge-invariant quantities at the EOB last stable circular orbit. Through this comparison, we have found some preliminary indications that the $overline{rm DJS}$ gauge might offer advantages in describing the inspiral dynamics of circularized binaries.
Roadmap for the Future
Looking ahead, there are several challenges and opportunities that lie on the horizon for the study of spin-orbit dynamics in binary systems:
- Further Investigations: The results presented in this study serve as a starting point for further investigations. It would be valuable to explore the implications of the $overline{rm DJS}$ gauge in more detail and compare its performance with other gauges in a wider range of scenarios.
- Numerical Simulations: While analytical advancements are crucial, numerical simulations can provide a more comprehensive understanding of spin-orbit dynamics. Future research should aim to combine analytical calculations with sophisticated numerical simulations to validate and refine theoretical models.
- Extensions to Higher Orders: The current study focuses on the third-subleading post-Newtonian corrections. Extending the analysis to even higher orders, such as the fourth-subleading or fifth-subleading post-Newtonian corrections, would provide a more accurate description of spin-orbit dynamics.
- Application to Realistic Systems: It is important to apply the theoretical advancements to realistic binary systems, such as black holes or neutron stars. Understanding the spin-orbit dynamics in these systems is relevant for gravitational wave astronomy and can provide insights into the properties of these astrophysical objects.
In conclusion, the recent progress in understanding spin-orbit dynamics in binary systems within the EOB formalism, specifically through the investigation of the DJS and $overline{rm DJS}$ gauges, opens up new avenues for future research. By delving deeper into these gauges, conducting numerical simulations, extending the analysis to higher orders, and applying the findings to realistic systems, we can continue to refine our understanding of spin-orbit dynamics and its implications for astrophysics.