arXiv:2411.09742v1 Announce Type: new
Abstract: The motion of compact binaries is influenced by the spin of their components starting at the 1.5 post-Newtonian (PN) order. On the other hand, in the large mass ratio limit, the spin of the lighter object appears in the equations of motion at first order in the mass ratio, coinciding with the leading gravitational self-force. Frame and gauge choices make it challenging to compare between the two limits, especially for generic spin configurations. We derive novel closed formulas for the gauge-invariant actions and frequencies for the motion of spinning test particles near Kerr black holes. We use this to express the Hamiltonian perturbatively in terms of action variables up to 3PN and compare it with the 1.5 PN action-angle Hamiltonian at finite mass ratios. This allows us to match the actions across both systems, providing a new gauge-invariant dictionary for interpolation between the two limits.
Future Roadmap: Challenges and Opportunities
Introduction
The motion of compact binaries and the effects of spin on their dynamics have been the subject of extensive research in gravitational physics. In this article, we examine recent findings that address the challenges of comparing the motion of spinning test particles near Kerr black holes in two different limits: the post-Newtonian (PN) limit and the large mass ratio limit. By deriving closed formulas for gauge-invariant actions and frequencies, the authors provide a new dictionary that allows for interpolation between these two limits. In this roadmap, we outline potential challenges and opportunities in this field for readers to explore.
1. Frame and Gauge Choices
One of the main challenges in comparing the PN and large mass ratio limits is the choice of frame and gauge. Frame and gauge choices can significantly impact the equations of motion and make it difficult to directly compare the two limits. Readers interested in this topic should investigate the various frame and gauge choices used in previous studies and their implications on the dynamics of spinning test particles.
2. Spin Configurations
An important aspect of the motion of spinning test particles is the configuration of their spins. Generic spin configurations further complicate the comparison between the PN and large mass ratio limits. Readers interested in this area of research should explore the effects of different spin configurations on the equations of motion and the challenges they pose in finding a consistent dictionary between the two limits.
3. Hamiltonian Perturbation
The derivation of gauge-invariant actions and frequencies provides a valuable tool for comparing the PN and large mass ratio limits. The perturbative expression of the Hamiltonian in terms of action variables up to 3PN allows for a direct comparison with the 1.5 PN action-angle Hamiltonian. Readers can delve into the details of this perturbation approach and its applicability in matching the actions across both systems.
4. Interpolation and New Dictionary
The derived closed formulas for gauge-invariant actions and frequencies serve as the foundation for establishing a new dictionary for interpolation between the PN and large mass ratio limits. Readers interested in this area should investigate the mathematical techniques used in this interpolation process and the accuracy of the matching between the two systems. Additionally, the potential implications of this new dictionary for future gravitational physics research should be explored.
Conclusion
The study of the motion of spinning test particles near Kerr black holes presents exciting challenges and opportunities in gravitational physics research. By addressing the challenges of frame and gauge choices, spin configurations, and establishing a new dictionary for interpolation, this article opens up avenues for further exploration in this field. Readers are encouraged to delve deeper into these topics, contributing to the ongoing understanding of the dynamics of compact binaries and the effects of spin on their motion.