Browsing by Author "Petrov, A.N."

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    Energy distribution for a spherically symmetric isolated system in general relativity
    (Plenum Publishing Corporation, 1996-07-09) Petrov, A.N.; Narlikar, J. V.
    The problems of the tolal energy and quasilocalenergy density or an isolated spherically symmetric static system in general relativity (GR) are considered with examples of some exact suintions. The field formulation of GR dereloped earlier hy L. P. Grishchuk. el al. (1984). in ihe framework of which all the dynamical fields, including the gravitation field, are considered in a fixed background spacetime is used intensively. The exact Schwarzschild and Reissner Nordstrom solutions are investigated in detail, and the results are compared with those in the recent work by J. D. Brown and J. W. York. Jr. (1993) as well as discussed with respect to the principle of nonlocalization of the gravitational energy in GR. Those examples are illustrative and simple because the background is selected as Minkowski spacetime and, in fact, the field configurations are studied in the framework of special relativity. It is shown that some problems of the Schwarzschild solution which are difficult to resolve in the standard geometrical framework of GR are resolved in the framework of the field formulation.
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    On the weakest falloff conditions in the metric for an isolated system
    (2015-01-27) Petrov, A.N.
    The weakest asymptotic behavior in the metric for defining an asymptotically fiat spacetime at spatial infinity is obtained. The technique of the field formulation of general relativity developed earlier in the Lagrangian description is used. The properties of the latter are similar to those of an ordinary gauge field theory in a fixed background spacetime. The role of the auxiliary background is plaid by Minkowski space. Integrals Of motion are defined with the help of a stress-energy tensor of the gravitational field together with its sources and Killing vectors of the background spacetime. It is shown that the weakest asymptotics of gauge transformations, which conserve values of the integrals of motion, defines the weakest falloff conditions in the field gravitational potentials (the same, in the dynamic metric of general relativity if the ordinary geometrical formulation is used). The results are compared with the some known ones.