R- and T-Regions in Space-Time with Spherically Symmetric Space

Details R- and T-Regions in Space-Time with Spherically Symmetric Space R- and T-Regions in Space-Time with Spherically Symmetric Space

Dec 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001gregr..33.2259n&link_type=abstract

General Relativity and Gravitation, v. 33, Issue 12, p. 2259-2295 (2001).

Mathematics

Logic

9

Scientific paper

The properties of solutions of Einstein's equations for spherically symmetric gravitational fields are studied. The notions of R- and T-universe regions are introduced. T-regions are shown to be regions of essential instability in the distinguished direction of the flow of time. The geometrical properties and those of the deformation of reference frames in these regions are discussed. Birkhoff's theorem for the Schwarzschild field is stated more precisely. In a T-region of this field there exists a frame of reference with the interval in the form ds^2 = left( {1 - {2{text{ }}m}/{c^3 t}} right)^{ - 1} c^2 dt^2 - left( {1 - {2{text{ }}m}/{c^3 t}} right)dr^2 - c^2 t^2 (d{text{ }}^{text{2}} + sin ^2 {text{ }}d{text{ }}^{text{2}} ), where t is the time coordinate, r the radial space coordinate, γ the Newtonian gravitational constant, c the fundamental velocity and m the mass producing the field. In this system, by comparison with Schwarzschild's, the space and time coordinates have changed places. The properties of the motion of light rays and test particles in R- and T-regions are discussed. The conclusions should be taken into account in considering cosmological questions and in the investigation of superdense stellar configurations.

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