Physics
Scientific paper
Sep 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977gregr...8..753r&link_type=abstract
General Relativity and Gravitation, vol. 8, Sept. 1977, p. 753-760. Research supported by the Deutsche Forschungsgemeinschaft.
Physics
4
Einstein Equations, Gravitational Fields, Matter (Physics), Relativity, Vacuum, Existence Theorems, Field Theory (Physics), Matching, Rotating Fluids, Schwarzschild Metric, Uniqueness Theorem
Scientific paper
Methods were recently developed for studying the problem of matching matter and vacuum solutions of Einstein's field equations along timelike hypersurfaces in the axisymmetric stationary case. Criteria for the existence and uniqueness of perfect-fluid sources for prescribed vacuum fields were given in the form of a theorem. As an application, the existence of such Kerr-interior solutions could be proved at least in a full neighborhood of suitably chosen boundary surfaces. In this paper further investigations of this 'matching problem' are made for some special cases. It is found that stationary rotating dust cannot be a source of the Kerr metric, and the existence of 'rotating Schwarzschild sources' is proved. These results are discussed together with further aspects of the general methods used.
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