The study of test-particle trajectories has a long history in physics and provides understanding into the properties of single black holes. With the recent breakthrough observation of gravitational waves, there has been renewed interest in investigating test-particle trajectories and developing new tools for calculations.
Jitze Hoogeveen awhile back released an article in which he investigated charged test-particle scattering and effective one-body metrics with spin using a novel approach to scattering angle calculation. This technique was adapted to the Kerr-Newman metric and an effective one-body theory with spin by the authors.
One of the key findings of this study was that electromagnetic situations are treatable, and the well-known Coulomb scattering angle can be readily obtained in resummed form in the weak field limit. Additionally, an effective one-body metric describing full binary motion may be constructed by explicitly matching scattering angles.
The authors also explored the application of the Newman-Janis Algorithm to the non-spinning effective one-body metric. In the non-spinning limit, their EOB formalism is related to previous approaches through a gauge-transformation of the post-geodesic Finsler-type Q term.
The study provides important insights into the behavior of charged test-particles in Kerr-Newman spacetime and demonstrates the potential of the effective one-body metric approach. The authors note that the EOB metric found in their study is by no means unique and that other solutions may exist based on different ansatz.
Furthermore, they leave to future work the extension to higher Post Minkowskian orders, by the inclusion of. This suggests that there is much more work to be done in this area, and future research could yield important insights into the properties of black holes and the behavior of test-particles in curved spacetime.
Overall, the importance of investigating test-particle trajectories and developing new calculational tools is underscored in this study. With the recent discovery of gravitational waves, there is renewed interest in this field, and new techniques and approaches are needed to truly understand the habits of test-particles in curved spacetime.
The findings of this study provide important insights into the behavior of charged test-particles in Kerr-Newman spacetime and demonstrate the potential of the effective one-body metric approach. It is likely that future research in this area will continue to yield important insights and contribute to our understanding of black holes and the properties of curved spacetime.