Further Study on the Conservation Laws of Energy-momentum Tensor Density for a Gravitational System

TL;DR

This paper thoroughly examines different methods of deriving Einstein conservation laws and energy-momentum tensors in gravitational systems, clarifies their equivalence, and discusses the energy-carrying nature of gravitational waves with new interpretations.

Contribution

It provides a detailed comparison of conservation laws, confirms their equivalence, and offers new insights into energy exchanges and gravitational wave energy transmission.

Findings

All methods for deriving Einstein conservation laws are equivalent.

Lorentz and Levi-Civita conservation laws are characterized and compared with Einstein laws.

PSR1913 does not confirm gravitational radiation according to the study.

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.