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Rational solutions of the Ernst equation. (English) Zbl 0810.35136
Shiohama, K. (ed.), Progress in differential geometry. Tokyo: Kinokuniya Company Ltd.. Adv. Stud. Pure Math. 22, 189-196 (1993).
Summary: We find infinitely many rational solutions of the Ernst equation in general relativity. These are constructed by solving a formal version of Hilbert’s homogeneous problem and are expressed in terms of determinants of Toeplitz type matrices.
For the entire collection see [Zbl 0779.00011].

35Q75 PDEs in connection with relativity and gravitational theory
35C05 Solutions to PDEs in closed form
83C15 Exact solutions to problems in general relativity and gravitational theory