Dynamical Hamilton Density of Gravitational Field

Abstract

Abstract. Following the recent study about "general transverse gauge condition" for gravity in weak field approximation in Ref [5], we revisit the energy density gauge-dependent problem of gravitational field by canonical field theory procedure in this paper. Firstly, we proof the general transverse gauge condition is meaningful and operational. Then by using the general transverse gauge condition, we can get the gauge-invariant solution of Einstein equation of general relativity. The final total Hamilton density of gravitational field obtained by our procedure shows some interesting properties: i) it is absolutely gauge-invariant and thus has no gauge-dependent problem. ii) It can be divided into two parts, pure dynamical and pure instantaneous. Just like what we had known the electromagnetic energy density in electrodynamics. iii) It differs from the traditional effective stress-energy tensor 00 1 2 hh , which may contribute some energy in total radiation system.