Ring singularity

In general relativity the gravitational singularity at the center of a rotating black hole (a "Kerr black hole") is supposed to form a circle rather than a point. This is often referred to as a ring singularity.

Description of a ring-singularity

When a spherical non-rotating body of a critical radius collapses under its own gravitation under general relativity, theory suggests it will 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 in classical physics (general relativity being a classical theory), 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, spacetime in the vicinity of the ring will undergo curvature in the direction of the ring's motion. Effectively this means that different observers placed around a Kerr black hole who are asked to point to the hole's apparent center of gravity may point to different points on the ring. Falling objects will begin to acquire angular momentum from the ring before they actually strike it, and the path taken by a perpendicular light ray (initially traveling toward the ring's center) will curve in the direction of ring motion before intersecting with the ring.

Traversability and nakedness

An observer crossing the event horizon of a non-rotating black hole cannot avoid the central singularity, which lies in the future world line of everything within the horizon. Thus one cannot avoid spaghettification by the tidal forces of the central singularity.

This is not necessarily true with a Kerr black hole. An observer falling into a Kerr black hole may be able to avoid the central singularity, by making clever use of the inner event horizon associated with this class of black hole. See the article on Kerr black holes for more detail. This makes it possible for the Kerr black hole to act as a sort of wormhole, possibly even a traversable wormhole.

Importance to wormhole theory

If a ring-singularity forms, and is traversable, it may hypothetically connect either two different universes, or two distant parts of the same universe. The path through the ring technically counts as a special class of wormhole.

It has been suggestedFact|date=February 2007that with two widely-separated Kerr-singularities, it is geometrically allowable that the rings could cross-connect, such that a traveler 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 one would go about constructing such a cross-connection.

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).

The Kerr singularity as a "toy" wormhole

The Kerr singularity can also be used as a mathematical tool to study the wormhole "field-line problem". If a particle is passed through a wormhole the continuity equations for the electric field suggest that the field-lines should not be broken.

By this argument, when an electrical charge passes through a wormhole, the particle's charge field-lines 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.)

Since a Kerr ring-singularity has the same feature, it also allows this issue to be studied.

Do ring singularities really exist?

It is generally expected that since the usual collapse to a point singularity under general relativity involves arbitrarily-dense conditions, that quantum effects may become significant and prevent the singularity forming ("quantum fuzz").

Even without quantum gravitational effects, there is good reason to suspect that the interior geometry of a rotating black hole is not the Kerr geometry. In 1960, Penrose pointed out that the inner event horizon of the Kerr geometry was probably not stable, due to the infinite blue-shifting of infalling radiation. (Penrose, 1960). This observation was supported by the work of other authors, such as (Possion and Israel, 1990), who investigated charged black holes which exhibited similar "infinite blueshifting" behavior. While much work has been done, the realistic gravitational collapse of objects into rotating black holes, and the resultant geometry, continues to be an active research topic. [http://arxiv.org/abs/gr-qc/9902008] [http://arxiv.org/abs/gr-qc/0103012] [http://arxiv.org/abs/gr-qc/9805008] [http://arxiv.org/abs/gr-qc/0304052] [http://arxiv.org/abs/gr-qc/9501003]

References

* Thorne, Kip, "", W. W. Norton & Company; Reprint edition, January 1, 1995, ISBN 0-393-31276-3.
*Matt Visser, "Lorentzian Wormholes: from Einstein to Hawking" (AIP press, 1995)
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ee also

*Black hole
*Black hole electron
*Gravitational singularity
*Geon (physics)
*Kerr black hole