Two-soliton stationary axisymmetric sprouts from Weyl seeds

Physics

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Scientific paper

The Belinskii-Zakharov inverse-scattering method is employed in its two-soliton version with a general Weyl seed, to obtain a stationary axisymmetric metric which in spheroidal coordinates of the Boyer-Lindquist type appears as a generalization of the Kerr-NUT solution. It contains several constants and two functions which can be found by integration from the seed potential (they can also be written as Legendre series). With a natural choice of parameters, the solution describes a reflectionally symmetric, asymptotically flat spacetime of a rotating black hole surrounded by a stationary axisymmetric source inherited from the seed. In a static limit, it goes over to a nonlinear superposition of the seed with a Schwarzschild black hole. A number of properties of the obtained class of solutions is given, in particular the characteristics of the horizon. For moderate angular momenta there seem to be no singularities on and outside the horizon. For a thin annular disc as the seed, the solution can represent a stationary thin annular disc around a rotating black hole.

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