Analytic Solutions for the Motion of Spinning Particles near Spherically Symmetric Black Holes and Exotic Compact Objects.

• DOI: 10.48550/arxiv.2308.00021
• Publication Date: 2024-04-23
• Authors: Vojtěch Witzany; Gabriel Andres Pi...
• Keywords: High Energy Physics - Theory; High Energy Physics - Theory (hep-th); FOS: Physical sciences; General Relativity and Quantum Cosmology (gr-qc); General Relativity and Quantum Cosmology

The notebooks and machine-readable formulas can be found in the repo https://github.com/VojtechW/Analytical-Solution-Spinning-particle-Spherical<br/>Rapidly rotating bodies moving in curved space-time experience the so-called spin-curvature force, which becomes important for the motion of compact objects in gravitational-wave inspirals. As a first approximation, this effect is captured in the motion of a spinning test particle. We solve the equations motion of a spinning particle to leading order in spin in arbitrary static and spherically symmetric space-times in terms of one-dimensional closed-form integrals. This solves the problem and proves its integrability in a wide range of modified gravities and near exotic compact objects. Then, by specializing to the case of bound orbits in Schwarzschild space-time, we demonstrate how to express the solution in the form of Jacobi elliptic functions.<br/>