Mathematics
Scientific paper
Apr 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007iaus..238..433p&link_type=abstract
Black Holes from Stars to Galaxies -- Across the Range of Masses. Edited by V. Karas and G. Matt. Proceedings of IAU Symposium #
Mathematics
Scientific paper
Linking together technology, observations, Einstein's theory and pure mathematics, black holes surrounded by disc-like structures prosper in some of the most interesting and violent sources in the universe - in galactic nuclei and X-ray binaries. However, a consistent exact description of the gravitational field of these systems is still lacking. In static axisymmetric case, the task reduces to Laplace equation and the fields of multiple sources follow by mere superposition, but in a rotating case, so relevant under the above astrophysical conditions, non-linearity of the field equations resists full grasp. Recently, mathematical methods developed in the theory of completely integrable systems seem to verge on explicit and satisfactory solutions to the Ernst version of the stationary axisymmetric Einstein's equations. Today referred to as methods of algebraic geometry, they seek them in terms of theta-functions on special manifolds which are - symptomatically - connected with the names of Riemann and Hilbert.
Pozar Norbert
Šácha J.
Semerak Oldřich
Zacek Miroslav
Zellerin T.
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