Inertial forces and photon surfaces in arbitrary spacetimes

Given, in an arbitrary spacetime (M, g), a two-dimensional timelike submanifold (SIGMA) and an observer field n on (SIGMA), we assign gravitational, centrifugal, Coriolis and Euler forces to every particle worldline (lambda) in (SIGMA) with respect to n. We prove that centrifugal and Coriolis forces vanish, for all (lambda) in (SIGMA) with respect to any n, if and only if (SIGMA) 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-Nordstrom spacetimes, and in Godel spacetime are worked out.