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Relative Gravitational Field and Conservation Laws in General Relativity
Author(s) -
Rylov Yu.
Publication year - 1963
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19634670702
Subject(s) - physics , gravitational field , general relativity , speed of gravity , equivalence principle (geometric) , classical field theory , gravitational redshift , gravitational time dilation , two body problem in general relativity , introduction to the mathematics of general relativity , gravitational energy , metric tensor , einstein tensor , stress–energy tensor , gravity probe a , classical mechanics , gravitation , conservation law , linearized gravity , exact solutions in general relativity , quantum mechanics , numerical relativity , riemann curvature tensor , geometry , geodesic , mathematics , curvature
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 E x ′ 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.