Analytic solutions for the motion of spinning particles near spherically symmetric black holes and exotic compact objects

TL;DR

This paper derives exact solutions for the motion of spinning particles in static, spherically symmetric spacetimes, including black holes and exotic objects, revealing integrability and explicit orbit expressions.

Contribution

It provides closed-form solutions for spinning particle trajectories in arbitrary static, spherically symmetric spacetimes, extending understanding of spin-curvature effects.

Findings

Solutions expressed as one-dimensional integrals

Proves integrability in various gravity theories

Explicit orbit solutions using Jacobi elliptic functions

Abstract

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.