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

Article

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

Witzany, V.; Piovano, G. A.

Phys. Rev. Lett. 132(17), 7 (2024)

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 spacetimes 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.

Institute authors

Witzany, Vojtěch

Supported by

PRIMUS/23/SCI/019 — Smrtonosný tanec: ovládnutí zpětné zářivé reakce poblíž černých děr pro gravitačně-vlnovou astronomii

BibTeX

@article{UTF1005,
  author        = {Witzany, V. and Piovano, G. A.},
  title         = {{Analytic Solutions for the Motion of Spinning Particles near Spherically Symmetric Black Holes and Exotic Compact Objects}},
  journal       = {Phys. Rev. Lett.},
  volume        = {132},
  number        = {17},
  pages         = {7},
  year          = {2024},
  month         = {4},
  doi           = {10.1103/PhysRevLett.132.171401},
  url           = {https://doi.org/10.1103/PhysRevLett.132.171401},
}