Inertial forces and photon surfaces in arbitrary spacetimes

TL;DR

This paper investigates the conditions under which inertial forces vanish on particle worldlines in arbitrary spacetimes, characterizing photon surfaces through geometric and physical criteria, with applications to various known spacetimes.

Contribution

It establishes a precise characterization of photon 2-surfaces via inertial force analysis and gyroscope transport, providing new criteria for their existence in general spacetimes.

Findings

Centrifugal and Coriolis forces vanish iff the worldsheet is a photon 2-surface.

Photon 2-surfaces are characterized by gyroscope transport properties.

Examples of photon 2-surfaces are constructed in multiple spacetime geometries.

Abstract

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.