Physical decomposition of gauge fields and gravitational field are interesting subjects for many researchers [1, 2, 3, 4]. The decomposition of gauge field in Refs[1,2,3] has successfully solved the two-decade gauge problem of a meaningful gluon spin. Ref[4] extended this method to the gravitational field and attacked the longstanding problem of gravitational energy density. The metric is unambiguously separated into a pure geometric term which contributes null curvature tensor, and a physical term which represents the true gravitational effect and always vanishes in a flat space-time. In this paper, we will find the static Schwarzschild solution in the physical decomposition of gravitational field. Moreover, we compare the above solution with the ordinary static Schwarzschild solution. The differences between them show that there perhaps exist some unknown gravitational field energy out of static gravitational source. This conclusion probably help us to find the graviton from the deep universe by the modern advanced doctors.
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 .
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