Nonrotating astronomical relativistic reference frames

The target of this paper is a discussion of the meaning of the Newtonian concept of a reference frame showing no rotation with respect to a set of distant celestial objects in the framework of general relativity. Because of the properties of Newtonian absolute space and time and the existence of global inertial reference systems in Newton's theory the theoretical construction of such a globally nonrotating reference frame is obvious. This definitively no longer is the case in a relativistic framework. There exist no global inertial reference systems and one faces the necessity to give the notion of nonrotating frames a rigorous meaning. Considering possible definitions of nonrotating reference frames in both Newtonian and relativistic physics, we conclude that the concept of relative spatial rotation between reference systems plays a fundamental role in defining nonrotating astronomical reference frames. It turns out that the property of two relativistic reference systems to show no spatial rotation relative to each other, being a coordinate-dependent concept, has some properties which cannot be interpreted within our "Newtonian common sense". As an example, we discuss two versions of a geocentric reference system, both of which can be considered to show no rotation relative to distant celestial objects at the present level of observational accuracy, but differing by a time-dependent rotation of considerable amplitude. Applying the obtained results to the recently elaborated formalisms for constructing relativistic astronomical reference systems, we describe relative spatial rotations between the galactic, barycentric, geocentric reference systems and the reference system of an observer. We find a certain parallel between the concept of simultaneity (synchronization of clocks) and the concept of reference system showing no rotation relative to distant celestial objects. Both notions are absolute in Newtonian physics and become coordinate-dependent in the relativistic framework, representing, therefore, a mathematical convention rather than a physically meaningful phenomena.