The Foundation of the Generalised Theory of Relativity
By A. Einstein.
From Annalen der Physik 4.49.1916.
The theory which is sketched in the following pages
forms the most wide-going generalization conceivable of
what is at present known as "the theory of Relativity;"
this latter theory I differentiate from the former
"Special Relativity theory," and suppose it to be known.
The generalization of the Relativity theory has been made
much easier through the form given to the special Relativity
theory by Minkowski, which mathematician was the
first to recognize clearly the formal equivalence of the space
like and time-like co-ordinates, and who made use of it in
the building up of the theory. The mathematical apparatus
useful for the general relativity theory, lay already complete
in the "Absolute Differential Calculus," which were
based on the researches of Gauss, Riemann and Christoffel
on the non-Euclidean manifold, and which have been
shaped into a system by Ricci and Levi-civita, and already
applied to the problems of theoretical physics. I have in
part B of this communication developed in the simplest
and clearest manner, all the supposed mathematical
auxiliaries, not known to Physicists, which will be useful
for our purpose, so that, a study of the mathematical
literature is not necessary for an understanding of this
paper. Finally in this place I thank my friend Grossmann,
by whose help I was not only spared the study of the
mathematical literature pertinent to this subject, but who
also aided me in the researches on the field equations of
gravitation.