2004/04/19 by Chris Doran, Anthony Lasenby, A. Lasenby +2 · 3 citations
Engineering · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Astrophysics (astro-ph) #Classical mechanics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #General relativity #Geophysics and Sensor Technology #Gravitation #Mathematical analysis #Mathematical physics #Mathematics #Minkowski space #Physics #Quantum mechanics #Relativity and Gravitational Theory #Schwarzschild radius #Singularity #Spacetime #astro-ph #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0404081
published in arXiv (Cornell University) (Cornell University) · 38 pages, 4 figures
arxiv created 2004/04/19 · openalex publication_date 2004/04/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Kerr-Schild solutions to the vacuum Einstein equations are considered from the viewpoint of integral equations. We show that, for a class of Kerr-Schild fields, the stress-energy 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 delta-function point source. For the Reissner-Nordstrom solution we find that inclusion of the gravitational fields removes the divergent self-energy 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 light-like path, as one expects for the endpoint of rotating, collapsing matter. Some implications of these results for physically-realistic black holes are discussed.