CZECHOSLOVAK JOURNAL OF PHYSICS Volume 51 · 2001 Number 8 · pp. 781–864 Odd-soliton solutions to the Einstein equations S. Chaudhuri ∗ ) Department of Physics, Gushkara Mahavidyalaya, Gushkara, Burdwan (W.B.), 713128, India K.C. Das Department of Physics, Katwa College, Katwa, Burdwan, 713130, India Received 9 May 2000; final version 9 October 2000 Using the Inverse Scattering Method (ISM) of Belinskii and Zakharov a new odd- soliton solutions to the Einstein’s field equations for an axially symmetric space-time in general relativity are obtained in the determinant form and shown to include Weyl’s half-integral delta static solutions in a special case. PACS : 04.20 Key words : General relativity, Einstein equations, odd-soliton solutions 1 Introduction The soliton technique, developed by Belinskii and Zakharov (BZ) [1,2], is very useful for generating solutions of Einstein’s field equations. Using the technique of BZ, we present in Section 2, vacuum n-soliton solutions to the Einstein’s field equations in the determinant form. In Section 3, odd n-soliton solutions of the Einstein’s field equations for stationary axisymmetric space-times are generated from an unphysical seed taken in the diagonal form and shown that in the static limit, the constructed solutions reduce to the Weyl’s half integral delta solutions. 2 Field equations The stationary axially symmetric metric can be written as ds 2 = g ab dx a dx b + f (dr 2 +dz 2 ) , (1) where the indices a, b take values 1,2. The metric coefficients g ab and f are functions of r, z only and t, φ = x 1 ,x 2 , respectively. The Einstein field equations for the metric * )Address for correspondence: Chaudhuri Lane, R.K. Palli, Badamtala, Burdwan (W.B.), 713101, India. Czech. J. Phys. Vol. 51 (2001) 781