Innermost stable circular orbits of spinning test particles in Schwarzschild and Kerr spacetimes
Abstract
We consider the motion of classical spinning test particles in Schwarzschild and Kerr metrics and investigate innermost stable circular orbits (ISCO). The main goal of this work is to find analytically the smallspin corrections for the parameters of ISCO (radius, total angular momentum, energy, orbital angular frequency) of spinning test particles in the case of vectors of black hole spin, particle spin and orbital angular momentum being collinear to each other. We analytically derive the smallspin linear corrections for arbitrary Kerr parameter a . The cases of Schwarzschild, slowly rotating and extreme Kerr black hole are considered in detail. For a slowly rotating black hole, the ISCO parameters are obtained up to quadratic in a and particle's spin s terms. From the formulas obtained it is seen that the spinorbital coupling has attractive character when spin and angular momentum are parallel and repulsive when they are antiparallel. For the case of the extreme Kerr black hole with corotating particle we succeed to find the exact analytical solution for the limiting ISCO parameters for arbitrary spin. It has been shown that the limiting values of ISCO radius and frequency do not depend on the particle's spin while values of energy and total angular momentum depend on it. We have also considered circular orbits of arbitrary radius and have found smallspin linear corrections for the total angular momentum, energy and frequency at given radius. System of equations for numerical calculation of ISCO parameters for arbitrary a and s is also explicitly written.
 Publication:

Physical Review D
 Pub Date:
 June 2015
 DOI:
 10.1103/PhysRevD.91.124030
 arXiv:
 arXiv:1503.07060
 Bibcode:
 2015PhRvD..91l4030J
 Keywords:

 04.20.q;
 04.25.g;
 Classical general relativity;
 Approximation methods;
 equations of motion;
 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 accepted to PhysRevD, 15 pages, 5 figures