Everybody knows Einstein's master work (The
general theory of relativity - GTR). Only few specialists remember exactly how
it has been built.
In that document we exhume E. B. Christoffel's
work [ (1869)] which is (i) continuing Riemann's
work (1864) and (ii) one of the mathematical pillars of the GTR.
We demonstrate that it can be applied either
for the preservation of the ds2 (the historical case) or for the invariance of
Planck's limit (see def.4.1) as well, without being obliged to be in contradiction
with the solutions of the GTR.
It turns out that, in doing so, we just
preserve the inverse of a non-degenerated 4D metric. The bonus of that
demonstration is a new family of electromagnetic fields (see equ.22) depending
on that metric and on its variations (see further developments on the next page).