Experimentally obtaining metrics in general relativity

TL;DR

This paper shows that metrics in general relativity can be obtained without solving Einstein's equations, using only geodesic observations and a defined interval unit, simplifying previous methods.

Contribution

It introduces a method to derive GR metrics from geodesic data without integrating Einstein's equations, building on historical approaches by Kretschmann and Lorentz.

Findings

Metrics can be obtained without Einstein equations

Observation of 10 geodesics suffices

Method simplifies previous derivations

Abstract

It seems to be not well known that the metrics of general relativity (GR) can be obtained without integrating Einstein equations. To that, we need only define a unit for GR-interval $\Delta s$, and observe 10 geodesics (out of which at least one must be nonnull). Even without using any unit, we can have $\kappa g_{\mu\nu}(x^\rho)$, where $\kappa=$const. Our notes attempt to simplify the articles of E. Kretschmann (1917) and of H.A. Lorentz (1923) about this last subject. The text of this article in English will soon be available, in LaTeX. Please ask the author. ----- /Sajne estas malmulte konata ke la metrikoj de /generala relativeco (/GR) povas esti havataj sen integri Einstein-ajn ekvaciojn. Por tio, ni bezonas difini nur unuon por /GR-tempo $\Delta s$, kaj observi 10 geodezajn (el kiuj, almena/u unu devas esti nenulan). E/c sen uzi iun unuon, ni povas havi $\kappa g_{\mu\nu}(x^\rho)$, kie $\kappa$=konst. Niaj notoj tentas simpligi la artikolojn de E. Kretschmann (1917) kaj de H.A. Lorentz (1923) pri tiu lasta afero.