Separation of variables and symmetry operators for the conformally invariant Klein-Gordon equation on curved spacetime
✍ Scribed by N. Kamran; R. G. McLenaghan
- Publisher
- Springer
- Year
- 1985
- Tongue
- English
- Weight
- 325 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0377-9017
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✦ Synopsis
The separability of the conformally invariant Klein-Gordon equation and the Laplace-Beltrami equation are contrasted on two classes of Petrov type D curved spacetimes, showing that neither implies the other. The second-order symmetry operators corresponding to the separation of variables of the conformally invariant Klein-Gordon equation are constructed in both classes and the most general secondorder symmetry operator for the conformally invariant Klein-Gordon operator on a general curved background is characterized tensorially in terms of a valence two-symmetric tensor satisfying the conformal Killing tensor equation and further constraints.