On the existence of interior solutions in general relativity
Abstract
The existence problem of matter sources for given stationary axisymmetric solutions of Einstein's vacuum field equations is investigated. The existence of sources of a differentially or rigidly rotating perfect fluid can be proved at least in the neighborhood of boundary surfaces if these can be chosen suitably (theorem). In particular, there exist such “halflocal” perfect fluid sources for the Kerr metric. Hence the existence of a global regular “Kerrinterior solution” cannot be excluded by local considerations in an arbitrarily small neighborhood of a possible boundary.
 Publication:

General Relativity and Gravitation
 Pub Date:
 May 1976
 DOI:
 10.1007/BF00766138
 Bibcode:
 1976GReGr...7..431R