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The geodesic flow of the BGPP metric is Liouville integrable

The geodesic flow of the BGPP metric is Liouville integrable

Authors :
Maciejewski, Andrzej J.
Przybylska, Maria
Valent, Galliano
Publication Year :
2023

Abstract

We prove that the geodesics equations corresponding to the BGPP metric are integrable in the Liouville sense. The $\mathrm{SO}(3,\mathbb{R})$ symmetry of the model allows to reduce the system from four to two degrees of freedom. Moreover, solutions of the reduced system and its degenerations can be solved explicitly or reduced to a certain quadrature. In degenerated cases BGPP metric coincides with the Eguchi-Hanson metric and for this case the mentioned quadrature can be calculated explicitly in terms of elliptic integrals.<br />Comment: 14 pages, one figure

Subjects

Subjects :
Mathematical Physics

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2302.02620
Document Type :
Working Paper
Full Text :
https://doi.org/10.1088/1361-6382/ace097