Local Origin of Hidden Symmetry in Rotating Spacetimes
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911627572412416 |
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| author | Kim, Hyeong-Chan |
| author_facet | Kim, Hyeong-Chan |
| contents | 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 Möbius, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08408 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local Origin of Hidden Symmetry in Rotating Spacetimes Kim, Hyeong-Chan General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory 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 Möbius, 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. |
| title | Local Origin of Hidden Symmetry in Rotating Spacetimes |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.08408 |