Geometric transport along circular orbits in stationary axisymmetric spacetimes.
Parallel transport along circular orbits in orthogonally transitive stationary axisymmetric spacetimes is described explicitly relative to Lie transport in terms of the electric and magnetic parts of the induced connection. The influence of both the gravitoelectromagnetic fields associated with the...
| Main Authors: | , , , |
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| Format: | |
| Language: | English |
| Published: |
2004
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| Online Access: | http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:177367 |
| Summary: | Parallel transport along circular orbits in orthogonally transitive stationary axisymmetric
spacetimes is described explicitly relative to Lie transport in terms of the electric
and magnetic parts of the induced connection. The influence of both the gravitoelectromagnetic
fields associated with the zero angular momentum observers and of the
Frenet-Serret parameters of these orbits as a function of their angular velocity is seen on
the behavior of parallel transport through its representation as a parameter-dependent
Lorentz transformation between these two inner-product preserving transports which is
generated by the induced connection. This extends the analysis of parallel transport in
the equatorial plane of the Kerr spacetime to the entire spacetime outside the black
hole horizon, and helps give an intuitive picture of how competing 'central attraction
forces' and centripetal accelerations contribute with gravitomagnetic effects to explain
the behavior of the 4-acceleration of circular orbits in that spacetime. |
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