Proceedings of the International Conference on Geometry, Integrability and Quantization

A Recursion Operator for Solutions of Einstein Field Equations

Tsukasa Takeuchi

Abstract

The (1,1)-tensor field on symplectic manifold that satisfies some integrability conditions is called a recursion operator. It is known the recursion operator is a characterization for integrable systems, and gives constants of motion for integrable systems. We construct recursion operators for the geodesic flows of some solutions of Einstein equation like Schwarzschild, Reissner-Nordström, Kerr and Kerr-Newman metrics.

Article information

Source
Proceedings of the Fifteenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Andrei Ludu and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2014), 249-258

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436815715

Digital Object Identifier
doi:10.7546/giq-15-2014-249-258

Mathematical Reviews number (MathSciNet)
MR3287762

Zentralblatt MATH identifier
1321.83014

Citation

Takeuchi, Tsukasa. A Recursion Operator for Solutions of Einstein Field Equations. Proceedings of the Fifteenth International Conference on Geometry, Integrability and Quantization, 249--258, Avangard Prima, Sofia, Bulgaria, 2014. doi:10.7546/giq-15-2014-249-258. https://projecteuclid.org/euclid.pgiq/1436815715


Export citation