  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.
