Energy Density of Gravitational Field in General Transverse Gauge

Abstract

In this paper, firstly, we will prove there is a general transverse gauge in general relativity for linear approximation. This gauge condition can play the same role as the radiation gauge condition in electrodynamics. It means that the non-physical metric tensor and affine connection can be removed by this general transverse gauge. Then, by using this gauge condition, the energy density of gravitational can be revisited. we prove that the energy distribution of pure gravitational field out of the source can be upgraded by using the Einstein, Weinberg and LandauLifshitz energy-momentum pseudo-tensors in general transverse gauge. Furthermore, the different parameter in general transverse gauge will bring some interesting conclusions, and these different results are also discussed detail in this paper. Finally, by the concrete computing the energy density of one gravitational source, we find the expression for Einstein is the most useful definition of energy-momentum in calculating energy density of gravity. This result successfully overcomes the last-standing problem of energy density of gravitational field . Keywordsgeneral relativity; transvers gauge;energymomentum; pseudo-tensors; energy density