Static observers in curved spaces and non-inertial frames in Minkowski spacetime

Abstract

Static observers in curved spacetimes may interpret their proper acceleration as the opposite of a local gravitational field (in the Newtonian sense). Based on this interpretation and motivated by the equivalence principle, we are led to investigate congruences of timelike curves in Minkowski spacetime whose acceleration field coincides with the acceleration field of static observers of curved spaces. The congruences give rise to non-inertial frames that are examined. Specifically, we find, based on the locality principle, the embedding of simultaneity hypersurfaces adapted to the non-inertial frame in an explicit form for arbitrary acceleration fields. We also determine, from the Einstein equations, a covariant field equation that regulates the behavior of the proper acceleration of static observers in curved spacetimes. It corresponds to an exact relativistic version of the Newtonian gravitational field equation. In the specific case in which the level surfaces of the norm of the acceleration field of the static observers are maximally symmetric two-dimensional spaces, the energy-momentum tensor of the source is analyzed.

Relativistic Quantum Clocks

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Simulating indefinite causal order with Rindler observers

“…Here we propose a method for simulating some specific indefinite causal structures, potentially in laboratory conditions, by utilizing the equivalence between stationary observers in the vicinity of the event horizon of a Schwarzschild black hole and Rindler observers in Minkowski space [15]. It is based on the generalization of Einstein's equivalence principle to spacetimes with indefinite metric structure by which we claim that quantum superposition of two macroscopically distinct metric structures of spacetime is locally equivalent to a "quantum reference frame" [16] in flat spacetime with two superposed proper accelerations.…”