Level sets of the lapse function in static GR

Abstract

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.

updated to published version. in D. Puetzfeld et al. (eds.), Equations of Motion in Relativistic Gravity, Fundamental Theories of Physics 179, Springer, 2015