  The various methods to derive Einstein conservation laws and the relevant
definitions of energy-momentum tensor density for gravitational fields are
studied in greater detail. It is shown that these methods are all equivalent.
The study on the identical and different characteristics between Lorentz and
Levi-Civita conservation laws and Einstein conservation laws is thoroughly
explored. Whether gravitational waves carry the energy-momentum is discussed
and some new interpretations for the energy exchanges in the gravitational
systems are given. The viewpoint that PSR1913 does not verify the gravitational
radiation is confirmed.
