Inertial forces and photon surfaces in arbitrary spacetimes
نویسندگان
چکیده
Given, in an arbitrary spacetime (M, g), a 2-dimensional timelike submanifold Σ and an observer field n on Σ, we assign gravitational, centrifugal, Coriolis and Euler forces to every particle worldline λ in Σ with respect to n. We prove that centrifugal and Coriolis forces vanish, for all λ in Σ with respect to any n, if and only if Σ 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-Nordström spacetimes, and in Gödel spacetime are worked out. PACS numbers: 04.20Cv 02.40Hw
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