Rotospheres in Stationary Axisymmetric Spacetimes

Abstract

Rotospheres are regions in spacetime where dynamics of angular motion may be related to kinematical parameters of the orbits in a counter-intuitive manner. Anomalous effects typically arise in rotation about a very compact source of gravity. We study them on circular orbits in a general asymptotically flat stationary axisymmetric spacetime. We relate the occurrence of counter-intuitive effects to the course of the limiting possible values of angular velocity and to that of the velocities of circular orbits nonaccelerated in a given direction, to conclude that rotospheres are always bounded by photon orbits. In the rotospheres, gyroscopes are shown to also precess in a “reverse” sense with respect to local important directions. The previously introduced “extremally accelerated observers” are presented as another natural generalization of “nonrotating” observers. A number of formulas are given that may be useful in analysing the test-particle dynamics and in the theory of measurements in stationary axisymmetric spacetimes; the formulae get especially simple in static fields. Also attached is a thorough list of references.