Editorial note to : T . Levi - Civita , The physical reality of some normal spaces of Bianchi and to : Einsteinian ds 2 in Newtonian fields . IX : The analog of the logarithmic potential

As mentioned in the accompanying biography, Levi-Civita and his teacher Ricci,1 prompted by Felix Klein, wrote an important review of tensor calculus (under the name of ‘absolute differential calculus’) in 1901 [1]. Einstein, advised by Marcel Grossmann, began to study this in 1912 and corresponded with Levi-Civita about it in the period leading up to the publication of the first paper on general relativity.2 Levi-Civita was thus well informed of Einstein’s work and had the mathematical tools to contribute to the field. He published many papers in the early years of general relativity (according to [2], about 40 in all) and engaged in popularization of the theory. While many of his papers are of interest, we have chosen here to present the two in which he gives the first publication of two very widely-used (and rediscovered) exact solutions in general relativity. The only other exact solutions papers before 1920 which are quoted in [3] are those of Schwarzschild, Droste and Reissner from 1916, of Weyl from 1917 and of Kottler and Nordström from 1918. Fuller discussions of both solutions can be found in [4], Sections 7.1 and 10.2.