Determination of coordinates in general relativity by a variational principle

In linear approximation coordinate systems will be used, which have small deviation from a cartesian coordinate system. By defining a measure of deviation and minimizing it, it is possible to introduce a coordinate system, which has minimal deviation from a cartesian system. The frame, established by this way, depends only on physical facts and boundary conditions as the example of Schwarzschild field in linear approximation shows. It turns out to be identical with the well known harmonic coordinates in this approximation. By this means an explanation is given for the application of just these coordinates. (author)