Level sets of the lapse function in static GR

We present a novel physical interpretation of the level sets of the (canonical) lapse function in static isolated general relativistic space-times. Our interpretation uses a notion of ‘constrained test particles’. It leads to a definition of gravitational force on test particles and to a previously unknown uniqueness result for the lapse function. In Section 5, we discuss ‘photon spheres’ in static isolated relativistic space-times and relate them to the level sets of the lapse function.