Killing tensors in pp-wave spacetimes

Details Killing tensors in pp-wave spacetimes Killing tensors in pp-wave spacetimes

2010-11-29

arxiv.org/abs/1011.6401v1

Class. Quantum Grav. 27 (2010) 245011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages

Scientific paper

The formal solution of the second order Killing tensor equations for the general pp-wave spacetime is given. The Killing tensor equations are integrated fully for some specific pp-wave spacetimes. In particular, the complete solution is given for the conformally flat plane wave spacetimes and we find that irreducible Killing tensors arise for specific classes. The maximum number of independent irreducible Killing tensors admitted by a conformally flat plane wave spacetime is shown to be six. It is shown that every pp-wave spacetime that admits an homothety will admit a Killing tensor of Koutras type and, with the exception of the singular scale-invariant plane wave spacetimes, this Killing tensor is irreducible.

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