Separation of Variables and Hamiltonian Formulation for the Ernst Equation

Korotkin, D. A.; Nicolai, Hermann

doi:10.1103/PhysRevLett.74.1272

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Separation of Variables and Hamiltonian Formulation for the Ernst Equation

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Nicolai, Hermann
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Korotkin, D. A., & Nicolai, H. (1995). Separation of Variables and Hamiltonian Formulation for the Ernst Equation. Physical Review Letters, 74(8), 1272-1275. doi:10.1103/PhysRevLett.74.1272.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-5BAE-E

Abstract

It is shown that the vacuum Einstein equations for an arbitrary stationary axisymmetric space-time can be completely separated by reformulating the Ernst equation and its associated linear system in terms of a nonautonomous Schlesinger-type dynamical system. The conformal factor of the metric coincides (up to some explicitly computable factor) with the τ function of the Ernst equation in the presence of finitely many regular singularities. We also present a canonical formulation of these results, which is based on a “two-time” Hamiltonian approach, and which opens new avenues for the quantization of such systems.