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2009

Spacetime Encodings III - Second Order Killing Tensors

Brink, Jeandrew

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This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing tensor.

The derivation of the spacetimes presented in this paper borrows from ideas about dynamical systems, and illustrates concepts that can be generalized to higher- order Killing tensors.
The relationship between the components of the Killing equations and metric functions are given explicitly.
The origin of the four separable coordinate systems found by Carter is explained and classified in terms of the analytic structure associated with the Killing equations.

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