6 papers
The Nakamura Conjecture Revisited: Toda Molecules and Stationary Axisymmetric Gravity
Takeshi Fukuyama
We revisit the Nakamura conjecture, which relates the Tomimatsu-Sato solutions of stationary axisymmetric gravity to finite Toda molecules. While the conjecture has been establishe…
Reduced Trilinear Reformulation of the Nakamura Conjecture
Takeshi Fukuyama
The Tomimatsu--Sato (TS) family, characterized by the rotation parameter and the TS index provides an important class of exact stationary axisymmetric vacuum solutions o…
Gauge Theory of Gravity and the AdS/CFT Correspondence
Takeshi Fukuyama
We discuss the AdS/CFT correspondence from the viewpoint of the gauge-theoretic formulation of gravity, in which gravity is interpreted as a broken phase of conformal gauge symmetr…
Evidence for Log-Periodic Modulation in the Redshift Distribution of High-Redshift Compact Sources
Takeshi Fukuyama
We investigate whether the redshift distribution of high-redshift compact sources identified in early James Webb Space Telescope (JWST) observations contains a statistically cohere…
Trilinear Kernel Structure and Its Gravitational Realization
Takeshi Fukuyama
We clarify the structural role of trilinear kernels in multidimensional integrable hierarchies and in stationary axisymmetric gravity. The Yu--Toda--Fukuyama (YTF) trilinear equati…
Tau--Function Multilinear Hierarchy of the Tomimatsu--Sato Spacetime: A Gravitational Realization of the YTSF Integrable Structure
Takeshi Fukuyama
The Tomimatsu--Sato (TS) family generalizes the Kerr black hole to higher multipole order and has long been regarded as algebraically complicated without any clear integrabilit…