Chronometric assessment of relativistic degrees of freedom of the gravity field

The relativistic gravity field has many more degrees of freedom than the Newtonian one. A single scalar potential, sourced by the mass density of matter only, is replaced by a metric - a symmetric and non-degenrate tensor field of rank two. It has ten components and is related, via Einstein's equation, to the energy momentum distribution on the spacetime. 

Some gravitational degrees of freedom in General Relativity can, again, be cast into at least two potentials that generalize the Newtonian geopotential. These concepts are utterly important to describe chronometric measurements, i.e., the comparison of clocks. They influence the redshift of a pair of standard clocks and the transformation between various time scales. Moreover, relativistic mass and spin multipole moments, in various definitions, are based upon those notions. Therefore, they are chosen to be fundamental quantities in chronometry.

In a framework of fully relativistic geodesy, we analyze the impact of, in particular, chronometric measurements on the determination of relativistic potentials and multipoles. The measurement prescription is given precisely and involved mathematical subtleties are made explicit. Genuine relativistic observables are defined and we relate the gravity degrees of freedom to observables to comment on, e.g., the impact on the relativistic definition of height, height system unifications, and deduced concepts such as the generalization of normal gravity and the reference ellipsoid.