Killing Tensors and Symmetries
David Garfinkle, (Physics Department, Oakland University, Rochester,, MI) E.N. Glass, (Physics Department, University of Michigan, Ann Arbor, MI)
TL;DR
The paper introduces a new, efficient method for identifying Killing tensors in spacetimes with symmetries, demonstrating its effectiveness on specific solutions and revealing their triviality.
Contribution
A novel method for finding Killing tensors that reduces computational effort and applies to general spacetimes, not limited to algebraically special cases.
Findings
All Killing tensors in Melvin's magnetic universe are trivial.
All Killing tensors in Schwarzschild vacuum are trivial.
The method is less computationally intensive than solving full equations.
Abstract
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.
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