"Separation of Variables and Hamiltonian Formulation for the Ernst Equation"

Details "Separation of Variables and Hamiltonian Formulation for the Ernst Equation" "Separation of Variables and Hamiltonian Formulation for the Ernst Equation"

1994-12-08

arxiv.org/abs/hep-th/9412072v1

Phys.Rev.Lett. 74 (1995) 1272-1275

Physics

High Energy Physics

High Energy Physics - Theory

LATEX, 12 pages, submitted to Physical Review Letters

Scientific paper

10.1103/PhysRevLett.74.1272

It is shown that the vacuum Einstein equations for an arbitrary stationary axisymmetric space-time can be completely separated by re-formulating the Ernst equation and its associated linear system in terms of a non-autonomous Schlesinger-type dynamical system. The conformal factor of the metric coincides (up to some explicitly computable factor) with the $\tau$-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.

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