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.
1998 Academic Press
1. Introduction
In very strong gravitational fields around spacetime singularities, there are regions where general relativity produces mechanical effects which, from the Newtonian viewpoint, appear strange and counter-intuitive. These include trapped regions and black holes, ergospheres, chronology and causality violating regions, repulsive domains. Recently much interest has been devoted to rotospheres, another peculiar strong-gravity regions, where several counter-intuitive effects arise connected with the rotation of matter about a central body.
Consider a test particle orbiting with an angular velocity | on a non-Keplerian circular orbit on constant radius r around a spherically symmetric body of mass M. In classical physics, the (signed specific) radial thrust the particle needs in order to follow a great circle, MÂr 2 &r| 2 , has a positive maximum at |=0 and falls to & with ||| increasing to + . In relativity, the picture may be partly or totally reverse in very strong fields. In the (spherically symmetric) Schwarzschild field, for example, the maintaining thrust of a circling particle reads -1&2MÂr (1&2MÂr&r 2 | 2 ) &1 (MÂr 2 &r| 2 ), which behaves in a classical manner above the radius r=3M of the circular photon orbit, but at each r<3M it has a positive Article No. PH975756 133 0003-4916Â98 25.00