Stability of circular orbits of spinning particles in Schwarzschild-like space–times

Abstract

Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space-times the equations of motion admit solutions representing circular orbits with particles spins being constant and normal to the plane of orbits. For the de Sitter background the orbits are always stable with particle velocity and momentum being co-linear along them. The world-line deviation equations for particles of the same spin-to-mass ratios are solved and the resulting deviation vectors are used to study the stability of orbits. It is shown that the orbits are stable against radial perturbations. The general criterion for stability against normal perturbations is obtained. Explicit calculations are performed in the case of the Schwarzschild space-time leading to the conclusion that the orbits are stable.

Hyperbolic-like elastic scattering of spinning particles by a Schwarzschild black hole

“…Most of the existing studies on spinning particle motion in a Schwarzschild spacetime concern either circular or eccentric orbits or even deviations due to spin from a reference orbit which is a circular geodesic (i.e., quasi-circular orbits) [22,23,24,25,26,27,28,29,30,31]. These results are useful when taking into account backreaction effects to the background metric, going beyond the test particle approximation by using, e.g., self-force techniques [32].…”

Dynamics of test bodies with spin in de Sitter spacetime

“…Furthermore, the use of the conserved quantities (2.11) appears to be quite useful also in situations when the number of Killing vectors is insufficient for the complete integration of the equations of motion, cf. for example the study of spinning bodies in the gravitational fields of the black body type sources in [54,55]. most important symbols used throughout the text.…”

Точні Рівняння Матісона−Папапетру Для Метрики Шварцшильда З Використанням Інтегралів Руху

“…Висвiтленню фiзичних ефектiв, зумовлених взаємодiєю спiну з гравiтацiйним полем згiдно з рiвняннями МП, придiлено значну увагу у роботах [28,29]. Зростає iнтерес до вивчення фiзичних наслiдкiв рiвнянь МП за останнi 10-12 рокiв [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. Зокрема, в [31] продовжено розпочате в [25] дослiдження можливостей проявiв хаосу в динамiчних системах за рахунок спiну; публiкацiї [38-40, 42, 45] присвяченi спiновим ефектам на колових орбiтах, у тому числi явищу прецесiї спiну [39,42], а [33][34][35] -"ефекту годинника".…”