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arXiv · 2104.02167

Killing tensors and photon surfaces in foliated spacetimes

Kirill Kobialko·Igor Bogush·Dmitri Gal'tsov
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Abstract

We present a purely geometric method for constructing a rank two Killing tensor in a spacetime with a codimension one foliation that lifts the trivial Killing tensors from slices to the entire manifold. The resulting Killing tensor can be nontrivial. A deep connection is found between the existence of such a Killing tensor and the presence of generalized photon surfaces in spacetime with two Killing vector fields. This technique generates Killing tensors in a purely algebraic way, without solving differential equations. The use of our method is demonstrated for Kerr, Kerr-Newman-NUT-AdS metrics and Kerr-NUT-AdS multicharge gauged supergravity solution.

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Kirill Kobialko, Igor Bogush, Dmitri Gal'tsov. 2021-04-05. Killing tensors and photon surfaces in foliated spacetimes. https://doi.org/10.1103/physrevd.104.044009

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