Inertial forces and photon surfaces in arbitrary spacetimes

Details Inertial forces and photon surfaces in arbitrary spacetimes Inertial forces and photon surfaces in arbitrary spacetimes

2003-06-10

arxiv.org/abs/gr-qc/0306042v1

Class.Quant.Grav. 20 (2003) 4635-4652

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, 2 eps-figures; submitted to Class. Quantum Grav

Scientific paper

10.1088/0264-9381/20/21/006

Given, in an arbitrary spacetime, a 2-dimensional timelike submanifold (worldsheet) and an observer field on this worldsheet, we assign gravitational, centrifugal, Coriolis and Euler forces to every particle worldline in the worldsheet with respect to the observer field. We prove that centrifugal and Coriolis forces vanish, for all particle worldlines with respect to any observer field, if and only if the worldsheet is a photon 2-surface, i.e., generated by two families of lightlike geodesics. We further demonstrate that a photon 2-surface can be characterized in terms of gyroscope transport and we give several mathematical criteria for the existence of photon 2-surfaces. Finally, examples of photon 2-surfaces in conformally flat spacetimes, in Schwarzschild and Reissner-Nordstroem spacetimes, and in Goedel spacetime are worked out.

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