Any coordinate system in GR?
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From: S. J. Crothers on 22 Sep 2006 15:13 The black hole was conceived through theory, not by any observations. It is alleged to be predicted by General Relativity. Thus, the issue is one of mathematics. This alleged object is dependent upon the validity of the tacit assumption that General Relativity requires of necessity that a singularity must only occur where the Riemann tensor scalar curvature invariant is unbounded. However, in the whole history of the subject, no relativist has ever proved this assumption. Indeed, it would appear that no relativist has even realised that this assumption requires proof. It requires proof. Will any one of those here who claim black holes are predicted by General Relativity provide a rigorous proof of their assumption? In the alternative, which is equivalent for the purpose, will any one of those here who claim that General Relativity predicts black holes provide a rigorous proof that a geometry is not entirely determined by the form of its line element? The requested proofs will of course require some actual original thinking, rather than a mere regurgitation of the standard relativist arguments which have always relied upon their assumption. I remark that it is rather easily proved that the standard assumption on the Riemann tensor scalar curvature invariant is false, so it will be interesting to see how a relativist here will handle the requested proof. |