Grossmann's help on general relativity

Galina Weinstein posted Genesis of general relativity - Discovery of general relativity

The intermediate stage of the development of general relativity is inseparable of Marcel Grossmann's mathematical assistance. Einstein acknowledges Grossmann's help during 1912-1914 to the development of general relativity. ...

Einstein and Grossmann's first joint paper entitled, "Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation" ("Outline of a Generalized Theory of Relativity and of a Theory of Gravitation") is called by scholars the "Entwurf" paper. ... Grossmann wrote the mathematical part of this paper and Einstein wrote the physical part. ...

The "Entwurf" theory was already very close to Einstein's general theory of relativity that he published in November 1915. The gravitational field is represented by a metric tensor, the mathematical apparatus of the theory is based on the work of Riemann, Christoffel, Ricci and Levi-Civita on differential covariants, and the action of gravity on other physical processes is represented by generally covariant equations (that is, in a form which remained unchanged under all coordinate transformations). ...

Scholars asked: Why did Einstein discard in winter 1912-1913 what appears in hindsight to be essentially the correct gravitational field equation, and what made his field equation acceptable in late 1915? Why did he reject equations of much broader covariance in 1912-1913? ... His rejection of the Ricci tensor need not be explained in terms of simple error. He was rather not prepared to accept generally covariant equations as a result of a number of misconceptions. ...

He introduced an ingenious argument – the Hole Argument – to demonstrate that generally covariant field equations were not permissible. The Hole Argument seemed to cause Einstein great satisfaction, or else he persuaded himself that he was satisfied. Having found the Hole argument, Einstein spent two years after 1913 looking for a non-generally covariant formulation of gravitational field equations.

The Einstein-Grossmann collaboration was one where Einstein wrote the wrong stuff and Grossmann wrote the correct stuff. Einstein argued for two years that Grossmann was wrong to require generally covariant field equations, even tho Levi-Civita explained the advantages of covariant equations, until David Hilbert eventually convinced Einstein of those equations.

Einstein's famous 1916 general relativity paper starts:

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. [1920 translation]

About half the paper is an explanation of tensor analysis. There is no reference to the Entwurf theory or Hilbert. The only papers cited were those by Einstein and K. Schwarzschild showing how Grossmann's covariant equations affect the precession of Mercury's orbit. The assistance from Levi-Civita and Grossmann is understated.

The Wikipedia article on general relativity mentions Einstein about 50 times, and says nothing about Grossmann or Hilbert. There is a lot more historical info at Relativity priority dispute.