On the general solutions of Hilbert-Einstein field equations in vacuum

Abstract

The Hilbert-Einstein field equations describe the structure of space-time in the general theory of relativity. Their simplified form, in a vacuum, was discovered in 1913 by Marcel Grossmann in two joint publications with Einstein, who, for his part, rejected this idea and presented another hypothesis... He reverted to Grossmann’s idea only two years later. The first known solution was that of Schwarzschild that provides the origin of the notion of a black hole. Let us also mention the Kerr solution, plane gravitational waves, the general first order solution, the successive approximations of the two black hole problem: hundreds of rigourous solutions are known today. The genesis of this discovery called for a series of curious coincidences. The absolute differential calculus was a speciality only of the School of Zurich, and it required an improbable meeting between this School, Albert Einstein and the mathematician Marcel Grossmann, who was also able to think as a pure physicist.