Local Origin of Hidden Symmetry in Rotating Spacetimes

Hyeong-Chan Kim

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arXiv · 2603.08408

Local Origin of Hidden Symmetry in Rotating Spacetimes

Hyeong-Chan Kim

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Abstract

We show that, within a broad stationary-axisymmetric class, Kerr-type separability and hidden symmetry arise as a local consequence of the Einstein equations. Without assuming separability, algebraic speciality, Killing--Yano symmetry, or global boundary conditions, we analyze stationary and axisymmetric geometries in a locally non-rotating orthonormal frame and impose a minimal local equilibrium condition, namely the absence of mixed energy-momentum fluxes. We find that the mixed Einstein equations enforce a rigid projective alignment between radial and angular sectors, uniquely characterized by a constant-Schwarzian constraint. This constraint yields a universal classification of local solutions into M\"obius, exponential, and trigonometric branches, of which global regularity selects precisely the Kerr-type sector. In this sense, the kinematical core of Kerr geometry is already fixed locally, and the Schwarzian structure provides the local origin of Kerr rigidity.

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Hyeong-Chan Kim. 2026-03-09. Local Origin of Hidden Symmetry in Rotating Spacetimes. https://arxiv.org/abs/2603.08408

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