Physics
Scientific paper
May 1955
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1955phrv...98..793b&link_type=abstract
Physical Review, vol. 98, Issue 3, pp. 793-800
Physics
6
Scientific paper
Using a second metric tensor γμν as proposed by Rosen, Gupta's supplementary condition for the gravitational field (which has the form of De Donder's coordinate condition) is written in general-covariant form. This supplementary condition appears to be of physical importance because of the use made of it by Gupta in the quantization of Einstein's gravitational field. This physical significance of the supplementary condition singles out a manifold of coordinate systems, which contains as sub-manifolds infinitely many metric spaces each allowing only "Lorentz transformations" leaving the γμν constant. A particle is called "at rest" if it is not accelerated with respect to some of these "Lorentz" frames. Although the γμν-metric may be important in the formulation of the quantum theory of gravitons, it does not enter in the line element describing the results of physical measurements of time or distance, which are described by a line element containing as metric the gravitational tensor gμν, so that space, flat with respect to hypothetical measurements by unrealistic rods keeping their γ-metric length on displacement, is actually found to be curved by physical measurements by realistic rods keeping their g-metric length on parallel displacement. The static spherically symmetric gravitational field gμν in empty space around a singularity "at rest" is obtained in terms of conventional polar coordinates in its "Lorentz" rest system, in a form satisfying the supplementary condition. A simple relation is established between this new solution and the Schwarzschild solution for this static central field. The radial coordinate ρ used in the Schwarzschild solution, which is a convenient variable in the discussion of planetary motion, differs by a constant from the polar coordinate r in the "Lorentz" frame in which the point source of the field is at rest. Neither r nor ρ is equal to the radial distance R measured from the point source. If a picture of space is made on the γ scale, then space has holes where masses are located. ("Swiss-cheese" model of space.) This fact may be helpful in eliminating divergencies of field theory.
No associations
LandOfFree
Use of the Flat-Space Metric in Einstein's Curved Universe, and the "Swiss-Cheese" Model of Space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Use of the Flat-Space Metric in Einstein's Curved Universe, and the "Swiss-Cheese" Model of Space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Use of the Flat-Space Metric in Einstein's Curved Universe, and the "Swiss-Cheese" Model of Space will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1306583