Toda Lattice and Tomimatsu-Sato Solutions
Takeshi FUKUYAMA, Kiyoshi Kamimura, Songju YU
TL;DR
This paper proves that solutions of the Toda molecule equation correspond to Tomimatsu-Sato solutions of Einstein's equations, using Pfaffian identities to establish the connection analytically.
Contribution
It provides an analytic proof linking Toda molecule solutions to Tomimatsu-Sato solutions, confirming Nakamura's conjecture with Pfaffian identities.
Findings
Complete proof for Weyl solutions
Partial proof for generic cases
Confirmation of Nakamura's conjecture
Abstract
We discuss an analytic proof of a conjecture (Nakamura) that solutions of Toda molecule equation give those of Ernst equation giving Tomimatsu-Sato solutions of Einstein equation. Using Pfaffian identities it is shown for Weyl solutions completely and for generic cases partially.
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