On Kruskal-Novikov co-ordinate systems

Details On Kruskal-Novikov co-ordinate systems On Kruskal-Novikov co-ordinate systems

Mar 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980ncimb..56...49g&link_type=abstract

Nuovo Cimento B, Serie 11, vol. 56B, Mar. 11, 1980, p. 49-71.

Mathematics

7

Astronomical Coordinates, Clock Paradox, Coordinate Transformations, Schwarzschild Metric, Space-Time Functions, Geodesic Lines, Singularity (Mathematics)

Scientific paper

The paper shows that when Kruskal-like or Novikov-like coordinate systems are developed in terms of physical quantities such as the maximum radius of radially moving geodesic clocks on the crossing radii of null geodesics at some Schwarzschild time coordinate T = constant line, one finds coordinate singularities in the metric, reflecting limitations in the coordinate system because of the manner of their construction. It is shown how the coordinate singularities can be removed from the metric by finding appropriate new mathematical coordinates, derived from the original physical quantities, in terms of which the metric appears to be free of singularities. Further, these mathematical coordinates turn out to be the Kruskal and Novikov coordinates. Also discussed are difficulties in determining the sense of future propagation of certain world-lines inside the Schwarzshild radius, suggesting that ideas leading to the black-hole concept should be reexamined.

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