Variational principles for energy-momentum tensors (Q1853818)

The paper gives some basic concepts of the standard variational formulation of the general relativity theory. The emphasis of this paper is put on analyzing the structure of Lagrangian for the first-order interactions, which, by author's definition, denotes the searched Lagrangian of a coupled physical problems ( such as electromagnetic field, perfect fluid, dust), and depends on the independent fields and their first derivatives. The Lagrangian for Einstein equations is obtained, some useful theorems are also provided in the paper.