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In General Relativity the Gravitational Singularity at the centre of a rotating Black Hole (a " Kerr Black Hole ") is supposed to form a circle rather than a point. Ths is often referred to as a ring singularity. DESCRIPTION OF A RING-SINGULARITY When a spherical non-rotating body collapses under its own Gravitation under general relativity, it is usually supposed to collapse to a single point. This is not the case with a rotating black hole (a Kerr Black Hole ). With a fluid rotating body, its distribution of mass is not Spherical (it shows an Equatorial Bulge ), and it has Angular Momentum . Since a point cannot support Rotation or angular momentum, the minimal shape of the singularity that can support these properties is instead a ring with zero thickness but non-zero radius, and this is referred to as a ring singularity, or '''Kerr singularity'''. Due to a rotating hole's rotational Frame-dragging effects, different observers placed around a Kerr black hole who are asked to point to the hole's apparent Centre Of Gravity may point to different points on the ring. TRAVERSABILITY AND NAKEDNESS If an observer dives into a nonrotating black hole one will be destroyed by Tidal Forces before one reaches the centre. Since gravitation at the singularity is always infinite, no matter how deep one goes, there will always be a gravitational Terminal Velocity greater than Lightspeed between the observer and the centre, and the presumed Point Singularity should always be concealed behind an observational horizon (the Cosmic Censorship Hypothesis ). This is not so obviously true with a Kerr black hole—an observer diving into one of these objects along the rotational axis may be able to reach the centre of the ring, from which point one may be able to look along the ring plane and see the singularity. Conventional physics arguments seem to break down at this point, and some writers have suggested that the entire circular surface bounded by the ring may be considered to be part of the singularity. IMPORTANCE TO WORMHOLE THEORY If a ring-singularity forms, and is traversable, then the universe that contains it now has two distinct and separate routes between any two spatial points, (1) around the singularity, and (2) through the singularity. Such a universe could be said to be Doubly Connected , and it can be argued that the path through the ring technically counts as a special class of Wormhole . However, this is an exceptionally boring variety of wormhole, since it connects two regions of spacetime that were already connected. Planar wormholes It has been suggested that with two widely-separated Kerr-singularities, it is geometrically allowable that the rings could cross-connect, so that a traveller could enter one ring and exit the other. This would then count as a class of singularity-bounded Planar Wormhole . It is not obvious how (or if) such a cross-connection could be created in real life. A singularity-bounded wormhole is of interest because it bypasses the usual assumption that a wormhole needs Exotic Matter producing a repulsive gravitational field to keep the wormhole throat open—in this case, our planar wormhole mouths only require an outward gravitational field in two dimensions (rather than three), and this is produced in effect by the outward-pointing Coriolis Field produced by the spinning mass (or by the "spinning" universe, depending on our Rotational Frame Of Reference ). ROTATING BLACK HOLES, TORI AND FUNDAMENTAL PARTICLES In this more advanced (and more hypothetical) wormhole scenario, both ring-singularities are "identified" and are effectively the same object. If we attempt to orbit the arm of part of a ring, we would find that instead of performing a 360-degrees rotation to return to our start point, we have to orbit it twice, 720 degrees, to get back to our starting point (ignoring additional distortion effects caused by the singularity's conventional gravitation). Various authors (mainstream and fringe) have experimented with the idea of a Black Hole Electron or suggested a Toroidal Topology For The Electron , John Wheeler has suggested that fundamental charged particles such as the electrons may be modelled as wormhole connections that trap lines of electric force. These suggestions are generally considered to be highly speculative. THE KERR SINGULARITY AS A "TOY" WORMHOLE The Kerr singularity can also be used as a mathematical tool to study the wormhole "fieldline problem". If a particle is passed through a wormhole, it has been suggested that the object's fieldlines pointing to its original position cannot disappear and reappear again at the far side of the wormhole, but should be "snarled up" on the geometry in a manner reminiscent of the way that someone walking a dog on a leash can may get the leash tangled around a Lamppost . By this argument, when an electrical charge passes through a wormhole, the particle's charge fieldlines appear to emanate from the entry mouth and the exit mouth gains a charge deficit. (For mass, the entry mouth gains mass and the exit mouth gets a mass deficit.) This problem is serious, since it suggests that perhaps the fieldline paradigm needs modification, or perhaps a particle entering a topological wormhole is unable to interact with anything on the far side, and sees itself to be in a single-ended cavity. Since a Kerr ring-singularity has the same problem, it allows this issue to be studied without the complicating issues of whether traversable wormholes really exist or not—under GR, ring singularities ''must'' exist, and ''can'' be created. DO RING SINGULARITIES REALLY EXIST? It is generally expected that since the usual collapse to a Point Singularity under GR involves arbitrarily-dense conditions, that Quantum Effects may become significant and prevent the singularity forming ("quantum fuzz"). If similar considerations prevent the formation of ring singularities, then the previous topological arguments may not be "physical". SEE ALSO Black Hole - Gravitational Singularity - Kerr Black Hole - Geon (physics) - Black Hole Electron REFERENCES
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