Optical reference geometry for stationary and static dynamics

Abstract

Attention is drawn to the advantages of representing dynamical behavior in a stationary or static background spacetime in terms of a fixed reference 3-geometry that differs from the usual one by a certain conformal rescaling factor. The resulting Riemannian metric may be appropriately described as the “optical geometry” in recognition of the fact that “line-of-sight” trajectories are faithfully represented within it as geodesic, at least in the strictly static case for which such “lines-of-sight” are unambiguously defined. (In more general stationary examples the geodesies represent what amounts to the result of a cancellation between the Coriolis-type effects that would cause a physical light path to deviate to one side or the other depending on the sense of propagation.) The application to the particular case of the Schwarzschild solution is discussed: In this example the optical 3-geometry has a throat that occurs not on the horizon (as in the directly projected 3-geometry) but at the radius of the circular null geodesic orbit.