A ring singularity or ringularity is the

gravitational singularity A gravitational singularity, spacetime singularity, or simply singularity, is a theoretical condition in which gravity is predicted to be so intense that spacetime itself would break down catastrophically. As such, a singularity is by defini ...

of a rotating

black hole A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. Th ...

, or a

Kerr black hole The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of gen ...

, that is shaped like a ring.

Description

When a spherical non-rotating body of a critical radius collapses under its own

gravitation In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...

under

general relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...

, theory suggests it will collapse to a 0-dimensional single point. This is not the case with a rotating black hole (a

). With a fluid rotating body, its distribution of mass is not

spherical A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

(it shows an

equatorial bulge An equatorial bulge is a difference between the equatorial and polar diameters of a planet, due to the centrifugal force exerted by the rotation about the body's axis. A rotating body tends to form an oblate spheroid rather than a sphere. On ...

), and it has

angular momentum Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of Momentum, linear momentum. It is an important physical quantity because it is a Conservation law, conserved quantity – the total ang ...

. Since a point cannot support

rotation Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an ''axis of rotation''. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersect ...

classical physics Classical physics refers to physics theories that are non-quantum or both non-quantum and non-relativistic, depending on the context. In historical discussions, ''classical physics'' refers to pre-1900 physics, while '' modern physics'' refers to ...

(general relativity being a classical theory), the minimal shape of the singularity that can support these properties is instead a 2D ring with zero thickness but non-zero radius, and this is referred to as a ringularity or Kerr singularity. A rotating hole's rotational

frame-dragging Frame-dragging is an effect on spacetime, predicted by Albert Einstein's General relativity, general theory of relativity, that is due to non-static stationary distributions of mass–energy. A stationary Field (physics), field is one that is ...

effects, described by the

Kerr metric The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of gen ...

, cause spacetime in the vicinity of the ring to 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 In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weighted relative position of the distributed mass sums to zero. For ...

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 In astrophysics, an event horizon is a boundary beyond which events cannot affect an outside observer. Wolfgang Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive c ...

of a non-rotating and uncharged black hole (a

Schwarzschild black hole In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumpti ...

) cannot avoid the central singularity, which lies in the future

world line The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept of modern physics, and particularly theoretical physics. The concept of a "world line" is distinguished from c ...

of everything within the horizon. Thus, one cannot avoid

spaghettification In astrophysics, spaghettification (sometimes referred to as the noodle effect) is the vertical stretching and horizontal compression of objects into long thin shapes (rather like spaghetti) in a very strong, non- homogeneous gravitational fi ...

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. This makes it theoretically (but not likely practically)Roy Kerr:
Spinning Black Holes
' (Lecture at the University of Canterbury, timecod
49m8s
/ref> possible for the Kerr black hole to act as a sort of

wormhole A wormhole is a hypothetical structure that connects disparate points in spacetime. It can be visualized as a tunnel with two ends at separate points in spacetime (i.e., different locations, different points in time, or both). Wormholes are base ...

, possibly even a traversable wormhole.

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. 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 density deficit due to

Bernoulli's principle Bernoulli's principle is a key concept in fluid dynamics that relates pressure, speed and height. For example, for a fluid flowing horizontally Bernoulli's principle states that an increase in the speed occurs simultaneously with a decrease i ...

. (For mass, the entry mouth gains mass density and the exit mouth gets a mass density deficit.) Since a Kerr singularity has the same feature, it also allows this issue to be studied.

Existence

It is generally expected that since the usual collapse to a point singularity under general relativity involves arbitrarily dense conditions,

quantum effects Quantum mechanics is the fundamental physical theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of a ...

may become significant and prevent the singularity forming ("quantum fuzz"). Without quantum gravitational effects, there is good reason to suspect that the interior geometry of a rotating black hole is not the Kerr geometry. The inner event horizon of the Kerr geometry is probably not stable, due to the infinite blue-shifting of infalling radiation. This observation was supported by the investigation of 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.

References

{{Black holes Black holes Wormhole theory Gravitational singularities

Description

Traversability and nakedness

As a toy wormhole

Existence

See also

Further reading

References