Relative Gravitational Field and Conservation Laws in General Relativity



It is shown that by a description of the gravitational field within the limits of Einstein's theory only a relative gravitational field, i. e. the gravitational field at a point x with respect to one at a point x′, is physically essential. A reflection of curved space-time into continuum of flat spaces Ex′ depending on coordinates of an arbitrary point x′ is made. The relative gravitational field is described by tensor potentials in terms of the two-metric formalism. The relative gravitational field depends on two points: on a current point x and a base point x′. This allows to localize the gravitational field without violating the equivalence principle. Integral conservation laws for energy momentum and angular momentum are obtained, the energy-momentum tensor being a true relative tensor, i. e. a tensor depending on two points: x and x′. All values connected with a gravitational field are relative what is interpreted as the presence of some general relativity in the gravitational field.