Soliton solution of Einstein field equations from non-diagonal seed (Q1189888)

Axially symmetric solutions of Einstein equations are obtained from a non-diagonal seed by inverse scattering method, first introduced by Belinsky and Zakharov. The paper starts with a brief outline of the method. Next, new solutions are obtained from non-diagonal seed solutions. Finally, the same seed metric is utilised in Nakamura's transformations and corresponding solutions to Einstein's equations are obtained. It is shown that the solution obtained from inverse scattering method is different from the solution obtained by Nakamura's procedure. [Reviewer's remark: The presentation of the paper is not upto the expectation. The paper is full of undefined quantities e.g., \(\omega\), \(\psi_ 0\), \(g_ 0\), \(g^ 1\), \(g\) (presumably matrix \(\{g_{ab}\})\), \({\mathcal M}_ c^{o(k)}\), \(U_ 0\), \(V_ 0\), etc., What about the compatibility of equations (6) and (7)? Superscripts and subscripts in equations (10-12) are neither defined nor matched].