Physics
Scientific paper
Nov 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984rspsa.396...55c&link_type=abstract
Royal Society (London), Proceedings, Series A - Mathematical and Physical Sciences (ISSN 0080-4630), vol. 396, no. 1810, Nov. 8,
Physics
62
Gravitational Waves, Space-Time Functions, Wave Interaction, Einstein Equations, Gauge Theory
Scientific paper
The equations appropriate for space-times with two space-like Killing-vectors are set up, ab initio, and explicit expressions for the components of the Riemann, the Ricci, and the Einstein tensors in a suitable tetrad-frame are written. The equations for the vacuum are reduced to a single equation of the Ernst type. It is then shown that the simplest linear solution of the Ernst equation leads directly to the Nutku-Halil solution for two colliding impulsive gravitational waves with uncorrelated polarizations. Thus, in some sense, the Nutku-Halil solution occupies the same place in space-times with two space-like Killing-vectors as the Kerr solution does in space-times with one time-like and one space-like Killing-vector. The Nutku-Halil solution is further described in a Newman-Penrose formalism; and the expressions for the Weyl scalars, in particular, make the development of curvature singularities manifest. Finally, a theorem analogous to Robinson's theorem (but much less strong) is proved for space-times with two space-like Killing-vectors.
Chandrasekhar Subrahmanyan
Ferrari Valeria
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