Static Observers in Curved Spaces and Non-inertial Frames in Minkowski Spacetime

摘要

Static observers in curved spacetimes may interpret their proper accelerationas the opposite of a local gravitational field (in the Newtonian sense). Basedon this interpretation and motivated by the equivalence principle, we are ledto investigate congruences of timelike curves in Minkowski spacetime whoseacceleration field coincides with the acceleration field of static observers ofcurved spaces. The congruences give rise to non-inertial frames that areexamined. Specifically we find, based on the locality principle, the embeddingof simultaneity hypersurfaces adapted to the non-inertial frame in an explicitform for arbitrary acceleration fields. We also determine, from the Einsteinequations, a covariant field equation that regulates the behavior of the properacceleration of static observers in curved spacetimes. It corresponds to anexact relativistic version of the Newtonian gravitational field equation. Inthe specific case in which the level surfaces of the norm of the accelerationfield of the static observers are maximally symmetric two-dimensional spaces,the energy-momentum tensor of the source is analyzed.