2025/12/02 by Takeshi Fukuyama, Fukuyama, Takeshi · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2512.03104
openalex publication_date 2025/12/02 · openalex created_date 2025/12/05 · openalex updated_date 2026/07/28
The Tomimatsu--Sato (TS) family generalizes the Kerr black hole to higher multipole order δ and has long been regarded as algebraically complicated without any clear integrability. We show instead that stationary axisymmetric vacuum Einstein equations, when the Ernst potential is written as a τ--ratio E=τ1/τ0, admit a universal decomposition of the Ernst numerator into a cubic part containing all second derivatives and a quartic gradient envelope. The cubic sector can be written in terms of Z3--symmetric trilinear Hirota operators, revealing a hidden integrable structure. For δ=2, using the explicit Tomimatsu--Sato polynomials, we verify that this trilinear sector coincides with a Yu--Toda--Sasa--Fukuyama (YTSF) equation-type kernel. Thus the TS geometry forms a gravitational realization of a multilinear τ--function hierarchy in stationary axisymmetric general relativity.