Integral equations, KerrSchild fields and gravitational sources
Abstract
KerrSchild solutions to the vacuum Einstein equations are considered from the viewpoint of integral equations. We show that, for a class of KerrSchild fields, the stressenergy tensor can be regarded as a total divergence in Minkowski spacetime. If one assumes that Minkowski coordinates cover the entire manifold (no maximal extension), then Gauss' theorem can be used to reveal the nature of any sources present. For the Schwarzschild and Vaidya solutions the fields are shown to result from a deltafunction point source. For the ReissnerNordstrom solution we find that inclusion of the gravitational fields removes the divergent selfenergy familiar from classical electromagnetism. For more general solutions a complex structure is seen to arise in a natural, geometric manner with the role of the unit imaginary fulfilled by the spacetime pseudoscalar. The Kerr solution is analysed leading to a novel picture of its global properties. Gauss' theorem reveals the presence of a disk of tension surrounded by the matter ring singularity. Remarkably, the tension profile over this disk has a simple classical interpretation. It is also shown that the matter in the ring follows a lightlike path, as one expects for the endpoint of rotating, collapsing matter. Some implications of these results for physicallyrealistic black holes are discussed.
 Publication:

arXiv eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:grqc/0404081
 Bibcode:
 2004gr.qc.....4081D
 Keywords:

 Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 38 pages, 4 figures