A class of conformally Einstein metrics

Details A class of conformally Einstein metrics A class of conformally Einstein metrics

Nov 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000cqgra..17.4765k&link_type=abstract

Classical and Quantum Gravity, Volume 17, Issue 22, pp. 4765-4776 (2000).

Physics

1

Scientific paper

A class of spacetime metrics with coefficients depending on a single null coordinate is introduced. The equation of the null cone at an arbitrary point is obtained in explicit form. It is shown that every metric in this class has a Weyl tensor of Petrov type N and is conformal to a metric satisfying the Einstein vacuum equations. The metrics belonging to a particular subclass are shown to be conformal to certain plane-wave solutions in general relativity. The properties of a generalization of these metrics to n + 1 dimensions are studied. The generalized metrics always have 2n-1 independent Killing vectors and 2n independent conformal Killing vectors. The algebra of Killing vectors turns out to be the Heisenberg algebra.

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