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