Variational Methods in General Relativity: Mitteleuropean Mathematical Inaccuracyand Italian Rigour. The Contribution of a. Palatini

摘要

The debate from 1915 to 1919 about the correct formulation of the variationalprinciple for gravitational field equations is discussed. The contributions of Einstein, Lorentz, Hilbert, Levi-Civita, and Palatini are analyzed. Palatini's attempts to develop a covariant variational approach to general relatively, with particular regard to the hypothesis in matter coupled with gravity, are reconstructed. His scientific works and private correspondence during the years 1920 to 1938 are summarized. The role played by Levi-Civita in Palatini's variational method is outlined. His method is discussed with special attention to the difficulties concerning the physically meaningless hypothesis regarding the dependence of the stress-energy tensor for matter in the gravitational potentials.