The Minkowski metric in non-inertial observer radar coordinates

We give a closed expression for the Minkowski (1+1)-dimensional metric in the radar coordinates of an arbitrary non-inertial observer O in terms of O's proper acceleration. Knowledge of the metric allows the non-inertial observer to perform experiments in spacetime without making reference to inertial frames. To clarify the relation between inertial and non-inertial observers the coordinate transformation between radar and inertial coordinates, also is given. We show that every conformally flat coordinate system can be regarded as the radar coordinate system of a suitable observer for a suitable parametrization of the observer worldline. Therefore, the coordinate transformation between arbitrarily moving observers is a conformal transformation and conformally invariant (1+1)-dimensional theories lead to the same physics for all observers, independently of their relative motion.Comment: Revtex4, 6 pages, 1 figur

Simultaneity and generalized connections in general relativity

Stationary extended frames in general relativity are considered. The requirement of stationarity allows to treat the spacetime as a principal fiber bundle over the one-dimensional group of time translations. Over this bundle a connection form establishes the simultaneity between neighboring events accordingly with the Einstein synchronization convention. The mathematics involved is that of gauge theories where a gauge choice is interpreted as a global simultaneity convention. Then simultaneity in non-stationary frames is investigated: it turns to be described by a gauge theory in a fiber bundle without structure group, the curvature being given by the Fr\"olicher-Nijenhuis bracket of the connection. The Bianchi identity of this gauge theory is a differential relation between the vorticity field and the acceleration field. In order for the simultaneity connection to be principal, a necessary and sufficient condition on the 4-velocity of the observers is given.Comment: RevTeX, 9 pages, 2 figures, 1 table. Previous title "The gauge nature of simultaneity". Classical and Quantum Gravity http://www.iop.org/EJ/journal/CQ