In

general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, a

**naked singularity** is a

gravitational singularityA gravitational singularity or spacetime singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system...

, without an

event horizonIn general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...

. In a

black holeA black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

, there is a region around the singularity, the

event horizonIn general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...

, where the gravitational force of the singularity is strong enough so that light cannot escape. Hence, the singularity cannot be directly observed. A naked singularity, by contrast, is observable from the outside.

The theoretical existence of naked singularities is important because their existence would mean that it would be possible to observe the collapse of an object to

*infinite density*. It would also cause foundational problems for general relativity, because in the presence of a naked singularity, general relativity cannot make predictions about the future evolution of spacetime.

Some research has suggested that if

loop quantum gravityLoop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...

is correct, then naked singularities could exist in nature, implying that the

cosmic censorship hypothesisThe weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of singularities arising in general relativity....

does not hold. Numerical calculations and some other arguments have also hinted at this possibility.

To this date, no naked singularities (and no event horizons) have been observed.

## Predicted formation

From concepts drawn of

rotating black holeA rotating black hole is a black hole that possesses spin angular momentum.-Types of black holes:There are four known, exact, black hole solutions to Einstein's equations, which describe gravity in General Relativity. Two of these rotate...

s, it is shown that a singularity, spinning rapidly, can become a ring-shaped object. This results in two event horizons, as well as an

ergosphereThe ergosphere is a region located outside a rotating black hole. Its name is derived from the Greek word ergon, which means “work”. It received this name because it is theoretically possible to extract energy and mass from the black hole in this region...

, which draw closer together as the spin of the singularity increases. When the outer and inner event horizons merge, they shrink toward the rotating singularity and eventually expose it to the rest of the universe.

A singularity rotating fast enough might be created by the collapse of dust or by a supernova of a fast-spinning star. Studies of

pulsarA pulsar is a highly magnetized, rotating neutron star that emits a beam of electromagnetic radiation. The radiation can only be observed when the beam of emission is pointing towards the Earth. This is called the lighthouse effect and gives rise to the pulsed nature that gives pulsars their name...

s and some computer simulations (Choptuik, 1997) have been performed.

This is, of course, an example of a mathematical difficulty (divergence to infinity of the density) which reveals a more profound problem in our understanding of the relevant physics involved in the process. A workable theory of

quantum gravityQuantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

should be able to solve problems such as these.

## Metrics

Disappearing event horizons exist in the

Kerr metricThe Kerr metric describes the geometry of empty spacetime around an uncharged axially-symmetric black-hole with an event horizon which is topologically a sphere. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which...

, which is a spinning black hole in a vacuum. Specifically, if the

angular momentumIn physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

is high enough the event horizons will disappear. Transforming the Kerr metric to Boyer-Lindquist coordinates, it can be shown that the

coordinate (which is not the radius) of the event horizon is

,

where

, and

. In this case, "event horizons disappear" means when the solutions are imaginary for

, or

.

Disappearing event horizons can also be seen with the Reissner-Nordström geometry of a charged black hole. In this metric it can be shown that the singularities occur at

,

where

, and

. Of the three possible cases for the relative values of

and

, the case where

causes both

to be imaginary. This means the metric is regular for all positive values of

, or in other words the singularity has no event horizon.

See

Kerr-Newman metricThe Kerr–Newman metric is a solution of the Einstein–Maxwell equations in general relativity, describing the spacetime geometry in the region surrounding a charged, rotating mass. It is assumed that the cosmological constant equals zero...

for a spinning, charged ring singularity.

## Effects

A naked singularity could allow scientists to observe an infinitely dense material, which would under normal circumstances be impossible by the cosmic censorship hypothesis. Without an event horizon of any kind, some speculate that naked singularities could actually emit light.

## Cosmic Censorship Hypothesis

The

cosmic censorship hypothesisThe weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of singularities arising in general relativity....

says that a naked singularity cannot arise in our universe from realistic initial conditions.

## External links

- Naked singularity on arXiv
The arXiv |Chi]], χ) is an archive for electronic preprints of scientific papers in the fields of mathematics, physics, astronomy, computer science, quantitative biology, statistics, and quantitative finance which can be accessed online. In many fields of mathematics and physics, almost all...

- M. C. Werner and A. O. Peters, "Magnification relations for Kerr lensing and testing cosmic censorship",
*Physical Review D*, Vol. 76, Issue 6 (2007).
- Pankaj S. Joshi, "Do Naked Singularities Break the Rules of Physics?",
*Scientific American*, January 2009.
- Marcus Chown, "Fast-spinning black holes might reveal all"
*New Scientist*, August 2009.