Relativistic spin–spin interaction of two concentric shells

Abstract

We investigate, in the framework of general relativity, a system consisting of two concentric shells of arbitrary thickness, spinning with angular velocity vectors ω and [Formula: see text], respectively. We use Einstein's linearized theory to define a total torque and total force acting on a body and find an interaction torque between the two bodies, proportional to [Formula: see text], which has no analogue in Newtonian mechanics.The angular velocity vectors of the earth's mantle and core make an angle of about 10−5 rad. With above system as a model for the earth, the relativistic interaction torque is about 4 × 1021 dyn cm.If a pulsar's crust and core have non-aligned axes of rotation, the relativistic torque alone will produce precession with a period of about 1 h.