Energy-Momentum of the Gravitational Field: Crucial Point for   Gravitation Physics and Cosmology
  A history of the problem of mathematical and physical definition for the energy-momentum of the gravity field is reviewed. As it was noted 90 years ago by Hilbert (1917), Einstein (1918), Schrodinger (1918) and Bauer (1918) within Geometrical Gravity approach (General Relativity) there is no tensor characteristics of the energy-momentum for the gravity field. Landau & Lifshitz (1971) called this quantity pseudo-tensor of energy-momentum and noted that Einstein's equations does not express the energy conservation for matter plus gravity field. This has crucial consequences for gravity physics and cosmology, such as negative energy density for static gravity field and violation of energy conservation in expanding space. However there is alternative Field Gravity approach for description of gravitation as a symmetric tensor field in Minkowski space, which is similar to description of all other physical interactions and based on well-defined positive, localizable energy-momentum of the gravity field. This relativistic quantum Field Gravity approach was partially developed by Firz & Pauli (1939), Birkhoff (1944), Thirring (1961), Kalman (1961), Feynman (1963) and others. Here it is shown that existence of well-defined positive energy-momentum of the gravity field leads to radical changes in gravity physics and cosmology, including such new possibilities as two-component nature of gravity - attraction (spin 2) and repulsion (spin 0), absence of black holes and singularities, scalar gravitational radiation caused by spherically symmetric gravitational collapse. 
Yu. V. Baryshev (Astron.Inst.St.-Petersburg Univ.)