On the "A Priori" Construction of Coordinates in General Relativity

Abstract

We construct by physical means the Schwarzschild coordinates for a static spherical-symmetric body, the canonical Weyl coordinates   for a static axial-symmetric body and the Weyl-Lewis-Papapetrou coordinates for a stationary axial-symmetric body. Because these coordinates are constructed before the equations of GR are solved , we speak of the " a priori " construction.  The symbols representing these coordinates in this way have a physical meaning. In the usual treatment the symbols representing the coordinates can have an alienating effect because only after the equations of GR are solved , thus " a posteriori " , their physical meaning can be unveiled.  For this reason the " a priori " construction contributes to the understanding of the theory. The definition of the second as the unit of time, the phenomena of gravitational time-delay and gravitational red-shift, some peculiarities of the Kerr-solution and the occurrences of coordinate-singularities are treated as illustrations.