Gravitomagnetism and relative observer clock effects

Abstract

The gravitomagnetic clock effect and the Sagnac effect for circularly rotating orbits in stationary axisymmetric spacetimes are studied from a relative observer point of view, clarifying their relationships and the roles played by special observer families. In particular, Semerák's recent characterization of extremely accelerated observers in terms of the two-clock clock effect is shown to be complemented by a similarly special property of the single-clock clock effect.

Gravitomagnetism in the Kerr Newman Taub NUT spacetime

“…Following up on our previous work [10], we have considered some of the main effects associated with the existence of a gravitomagnetic monopole moment. The time coordinate t is periodic in the KNTN spacetime with a period that is simply proportional to the gravitomagnetic monopole moment of the source.…”

“…Thus if t + (t − ) denotes the coordinate time period for a complete revolution around the black hole in the counterclockwise (clockwise) sense ( φ = ±2π), then 13) which is the expression for the single-clock clock effect [10,11] in this case. Note that as r → ∞ this result reduces to 14) so that the effect is always less than 4πa, the result for a neutral particle.…”

“…Note that as r → ∞ this result reduces to 14) so that the effect is always less than 4πa, the result for a neutral particle. It is interesting to investigate the two-clock clock effect [10,11] in this case as well, i.e. τ + − τ − , where τ is the corresponding proper time as measured along the geodesics.…”

Geometric Transport Along Circular Orbits in Stationary Axisymmetric Spacetimes

“…This allows a study of clock effects, 18 i.e., comparing periods of counter-revolving orbits defined in various ways, as well as circular holonomy. Parallel transport of an initial vector along such an orbit leads to a variable rotation or boost in an invariant stationary axisymmetric 2-plane relative to the corresponding Lie dragged vector.…”

Holonomy Transformation in the Lense-Thirring Spacetime

“…Among other calculations of this quantity, we can mention the one corresponding to a class of topological defects 5 and others spacetimes [6][7][8][9][10][11][12][13][14][15] .…”