Axially Symmetric, Stationary Gravitational Field Equations and Pseudospherical Surfaces

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Abstract
For axially symmetric, stationary gravitational field equations, a new Lax pair of the inverse scattering method is presented from a geometrical point of view. The metric coefficient e2r(= − gρρg−1tt) is taken as the basic field variable, which satisfies an equation describing pseudospherical surfaces, i.e., surfaces of constant negative Gaussian curvature. The equations for other metric coefficients are also discussed.

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