Fermi Normal Coordinates and Fermion Curvature Couplings in General Relativity

Abstract

We study gravitational curvature effects in circular and radial geodesics in static, spherically symmetric space-times, using Fermi normal coordinates. We first set up these coordinates in the general case, and then use this to study effective magnetic fields due to gravitational curvature in the exterior and interior Schwarzschild, Janis-Newman-Winicour, and Bertrand space-times. We show that these fields can be large for specific parameter values in the theories, and thus might have observational significance. We discuss the qualitative differences of the magnetic field for vacuum space-times and for those seeded by matter. We estimate the magnitude of these fields in realistic galactic scenarios and discuss their possible experimental relevance. Gravitational curvature corrections to the Hydrogen atom spectrum for these space-times are also discussed briefly.