Innermost stable circular orbits of spinning test particles in\n Schwarzschild and Kerr space-times

2015/03/24 by Paul I. Jefremov, Jefremov, Paul I., Oleg Yu. Tsupko +3 · 7 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Pulsars and Gravitational Waves Research #Relativity and Gravitational Theory

paper · pdf · doi:10.48550/arxiv.1503.07060

openalex publication_date 2015/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the motion of classical spinning test particles in Schwarzschild\nand Kerr metrics and investigate innermost stable circular orbits (ISCO). The\nmain goal of this work is to find analytically the small-spin corrections for\nthe parameters of ISCO (radius, total angular momentum, energy, orbital angular\nfrequency) of spinning test particles in the case of vectors of black hole\nspin, particle spin and orbital angular momentum being collinear to each other.\nWe analytically derive the small-spin linear corrections for arbitrary Kerr\nparameter a. The cases of Schwarzschild, slowly rotating and extreme Kerr\nblack hole are considered in details. For a slowly rotating black hole the ISCO\nparameters are obtained up to quadratic in a and particle's spin s terms.\nFrom the formulae obtained it is seen that the spin-orbital coupling has\nattractive character when spin and angular momentum are parallel and repulsive\nwhen they are antiparallel. For the case of the extreme Kerr black hole with\nco-rotating particle we succeed to find the exact analytical solution for the\nlimiting ISCO parameters for arbitrary spin. It has been shown that the\nlimiting values of ISCO radius and frequency do not depend on the particle's\nspin while values of energy and total angular momentum depend on it. We have\nalso considered circular orbits of arbitrary radius and have found small-spin\nlinear corrections for the total angular momentum and energy at given radius.\nSystem of equations for numerical calculation of ISCO parameters for arbitrary\na and s is also explicitly written.\n

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