A proposed source for the Kerr black hole geometry and the geodesic property of cosmic strings.

摘要

source for the Kerr black hole geometry is presented. The source consists of a toroidal shell that encloses the ring singularity, a disc that spans the equatorial plane and an annulus of matter interior to the torus. The torus is also filled with some matter that gives negligible contributions to the overall mass and angular momentum of the source. The disc and annulus contribute negative masses and angular momenta. The toroidal shell gives positive values. The source as a whole gives the correct values for the mass and angular momentum of a Kerr black hole.;The work on the Kerr black hole is extended to the Kerr-Newman black hole. The source for the Kerr-Newman black hole geometry is very similar to that for the Kerr black hole. Additional care must be taken to account for the effect of the electromagnetic field. The source gives the correct values for the mass, angular momentum. and electric charge of a Kerr-Newman black hole.;Spacetime splittings are also examined. The ADM 3 + 1 spacetime split is extended to a generalised m + n splitting of spacetime. The global spacetime has dimension (m + n) and the foliating spaces have dimension m. There are n independent normals to each of these foliating spaces, thus giving n distinct extrinsic curvatures. The generalised Gauss-Weingarten and the generalised Gauss-Codazzi equations associated with this splitting are derived. Both these sets of generalised equations are shown to reduce to the familar ADM equations when a 3 + 1 split is considered. In the case of an orthogonal splitting, the generalised equations are found to exhibit a particularly elegant form.;Finally, the geodesic properties of cosmic strings are investigated. It is shown that idealised cosmic strings deform the background geometry in such a way that they become geodesics of spacetime. For deficit angles less than