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arXiv · 2507.11215

On the Yamazaki-Hori solution of the Ernst equation

A. Melikyan
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Abstract

A family of solutions to the Ernst equation is presented, which, in a certain limit, recovers the Yamazaki-Hori solution - an extension of the Tomimatsu-Sato solutions for all integer values of the deformation parameter $\delta$. Our solution also recovers, as a special case, the formulation given by Vein, which is equivalent to the Yamazaki-Hori solution. Furthermore, our construction establishes a connection to a nonlinear differential equation proposed by Cosgrove, which is also associated with the Ernst equation.

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A. Melikyan. 2025-07-15. On the Yamazaki-Hori solution of the Ernst equation. https://arxiv.org/abs/2507.11215

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