Mathematics
Scientific paper
Jun 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986gregr..18..557s&link_type=abstract
General Relativity and Gravitation (ISSN 0001-7701), vol. 18, June 1986, p. 557-583.
Mathematics
29
Geodesic Lines, Relativistic Theory, Singularity (Mathematics), Space-Time Functions, Coordinates, Curvature, Curves (Geometry), Scalars
Scientific paper
The directional singularity of Curzon (1924) in the Weyl metric is investigated analytically, first in t = constant spatial sections and then globally in space-time. In the spatial coordinate system developed, the singularity appears as an unambiguous ring, through which spatial geodesics can approach a spacelike infinity lying beyond the ring. Then the behavior of all (timelike, null, and spacelike) geodesics approaching R = 0 is reviewed; a new global coordinate system exhibiting all the spatial features and permitting extension of the relevant geodesics is constructed; and it is shown that the Curzon metric can be smoothly connected with Minkowski space in this system. It is concluded that the Curzon solution can be viewed as a sandwich-wavelike development out of Minkowski space or as the end product of a nonspherical collapse. Diagrams and tables are included.
Scott Susan M.
Szekeres Peter
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