Further Study on the Conservation Laws of Energymomentum Tensor Density for a Gravitationa.pdf

Further Study on the Conservation Laws of Energy-momentum Tensor Density for a Gravitational System Chen Fang-Pei Department of Physics, Dalian University of Technology, Dalian 116024, China. E-mail: chenfap@dlut.edu.cn Abstract 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. Keyword: Energy-momentum tensor; Conservation laws; Gravitational waves Binary pulsar; PSR1913 PACS number: 04.20.Cv; 04.30.-w; 04.90.+e 1. Introduction There exist the following two kinds of conservation laws of energy-momentum tensor density for a gravitational system [1, 2, 3]: I, Lorentz and Levi-Civita conservation laws ∂ µ µ ( −g T + −g T ) 0 (1) ∂x µ (M )α (G )α −g T µ + −g T µ 0 (2) (M )α (G )α II, Einstein conservation laws ∂ µ ~µ ∂x µ ( −g T (M )α + −g t(G )α ) 0 (3) In Eq.(1), −g T µ