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

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.

The notebooks and machine-readable formulas can be found in the repo https://github.com/VojtechW/Analytical-Solution-Spinning-particle-Spherical

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Cited by in corpus (17)

• The Science of the Einstein Telescope
• Scattering and bound observables for spinning particles in Kerr spacetime with generic spin orientations
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• Spinning particles near Kerr black holes: Orbits and gravitational-wave fluxes through the Hamilton-Jacobi formalism
• Analytic Solution for the Motion of Spinning Particles in Kerr Space-Time
• Dynamics of spinning particles in Reissner-Nordström black hole exterior
• Post-Newtonian expansions of extreme mass ratio inspirals of spinning bodies into Schwarzschild black holes
• Post-adiabatic waveform-generation framework for asymmetric precessing binaries
• Symplectic mechanics of relativistic spinning compact bodies II.: Canonical formalism in the Schwarzschild spacetime
• Particle dynamics and optical appearance of charged spherically symmetric black holes in bumblebee gravity
• Analytical model of precessing binaries using post-Newtonian theory in the extreme mass-ratio limit I: General Formalism
• Geodesic Motion of Test Particles around the Scalar Hairy Black Holes with Asymmetric Vacua
• Spherical inspirals of spinning bodies into Kerr black holes
• Analytic solutions for the motion of spinning particles near brane-world black hole
• Gauss-Bonnet lensing of spinning massive particles in static spherically symmetric spacetimes
• The precession of particle spin in spherical symmetric spacetimes
• Particles with precessing spin in Kerr spacetime: analytic solutions for eccentric orbits and homoclinic motion near the equatorial plane