An approach to generation of new solutions for gravitational field equations with Riemann-Hilbert method. (Chinese. English summary) Zbl 0704.53075
Summary: For the Ernst equation of gravitational fields we give finite transformations of the Virasoro group by means of the formalism of Cauchy integral equations from the Riemann-Hilbert problem, and establish the representations of the semidirect product of Virasoro and Kac-Moody groups which are non-unitary and of no highest weight. The transformations of the semidirect product group generate new solutions from the known ones. We also assert that many known transformations, such as Neugebauer’s Bäcklund transformation, are subgroups or subsets of the group.
MSC:
| 53C80 | Applications of global differential geometry to the sciences |
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 81R10 | Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations |
