# Inertial forces and photon surfaces in arbitrary spacetimes

Foertsch, T; Hasse, W; Perlick, V (2003). Inertial forces and photon surfaces in arbitrary spacetimes. Classical and Quantum Gravity, 20(21):4635-4651.

## Abstract

Given, in an arbitrary spacetime (M, g), a two-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.

## Abstract

Given, in an arbitrary spacetime (M, g), a two-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.

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