Gyroscopic Precession and Inertial Forces in Axially Symmetric Stationary Spacetimes

We study the phenomenon of gyroscopic precession and the analogues of inertial forces within the framework of general relativity. Covariant connections between the two are established for circular orbits in stationary spacetimes with axial symmetry. Specializing to static spacetimes, we prove that gyroscopic precession and centrifugal force both reverse at the photon orbits. Simultaneous non-reversal of these in the case of stationary spacetimes is discussed. Further insight is gained in the case of static spacetime by considering the phenomena in a spacetime conformal to the original one. Gravi-electric and gravi-magnetic fields are studied and their relation to inertial forces is established.     

Gyroscopic Precession and Centrifugal Force in the Ernst Spacetime

The phenomenon of gyroscopic precession in the Ernst spacetime is studied within the framework of the Frenet-Serret formalism. General formulae are obtained for circular orbits. At the same time general relativistic analogues of inertial forces such as gravitational and centrifugal forces are also investigated in the Ernst spacetime. Reversal of gyroscopic precession as well as centrifugal force is considered at the circular photon orbits. These phenomena are examined in the Melvin universe as a special case of the Ernst spacetime by setting the mass parameter equal to zero.