Gyroscopic Precession and Inertial Forces in Axially Symmetric Stationary Spacetimes

TL;DR

This paper explores gyroscopic precession and inertial forces in stationary, axially symmetric spacetimes within general relativity, revealing conditions for their reversal and connections to gravitational fields.

Contribution

It establishes covariant links between gyroscopic precession and inertial forces for circular orbits, especially analyzing reversal phenomena in static and stationary spacetimes.

Findings

Gyroscopic precession and centrifugal force reverse at photon orbits in static spacetimes.

Simultaneous non-reversal occurs in stationary spacetimes.

Gravi-electric and gravi-magnetic fields are related to inertial forces.

Abstract

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.