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Killing tensors and symmetries. (English) Zbl 1190.83025

Summary: A new method is presented for finding Killing tensors in spacetimes with symmetries. The method is used to find all the Killing tensors of Melvin’s magnetic universe and the Schwarzschild vacuum. We show that they are all trivial. The method requires less computation than solving the full Killing tensor equations directly, and it can be used even when the spacetime is not algebraically special.

MSC:

83C15 Exact solutions to problems in general relativity and gravitational theory
83C57 Black holes
53Z05 Applications of differential geometry to physics
83F05 Relativistic cosmology
83C75 Space-time singularities, cosmic censorship, etc.
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