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Circular Orbits in Stationary Axisymmetric Spacetimes

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Abstract

Several types of characteristics of spatially circular timelike trajectories in stationary axisymmetric spacetimes are related in a simple and covariant manner. The relations allow us to establish straightforward links between different phenomena often studied on circular orbits: mechanics of a single test particle, precession of gyroscopes with respect to important vectors defined along the orbit, geometrical parameters (curvatures) of the trajectory provided by the Frenet-Serret formalism, and geometrical properties (vorticity and shear) of the whole circular congruence.

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Semerák, O. Circular Orbits in Stationary Axisymmetric Spacetimes. General Relativity and Gravitation 30, 1203–1215 (1998). https://doi.org/10.1023/A:1026694811879

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