Computer Science
Scientific paper
Jan 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cqgra...2...87m&link_type=abstract
Classical and Quantum Gravity (ISSN 0264-9381), vol. 2, Jan. 1, 1985, p. 87-97. Research supported by the British Council and Ro
Computer Science
19
Einstein Equations, Gravitation Theory, Gravitational Waves, Metric Space, Relativity, Space-Time Functions, Collinearity, Conformal Mapping, Curvature, Symmetry, Vacuum
Scientific paper
The types of symmetry (including curvature collineations, special conformal motions, homothetic motions, and null and nonnull symmetry-vector-field motions) inherent in metrics which are solutions of the Einstein vacuum equations are investigated in an analytical review. The results are compiled in a table, and it is shown that a vacuum metric with a nontrivial conformal motion must be a pp-wave metric. Special consideration is given to twisting type-N metrics which have both homothetic and isometric motions: the Hauser (1974) metric is found to be the only exact solution admitting such a two-parameter group, and the generalized metric is formulated as the solution of a sixth-order ordinary differential equation with a constraint equation.
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