In
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, a naked singularity is a hypothetical
gravitational singularity
A gravitational singularity, spacetime singularity or simply singularity is a condition in which gravitational field, gravity is so intense that spacetime itself breaks down catastrophically. As such, a singularity is by definition no longer p ...
without an
event horizon
In astrophysics, an event horizon is a boundary beyond which events cannot affect an 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 compact obj ...
. In a
black hole
A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
, the singularity is completely enclosed by a boundary known as the
event horizon
In astrophysics, an event horizon is a boundary beyond which events cannot affect an 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 compact obj ...
, inside which the curvature of
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
caused by the singularity is so strong that light cannot escape. Hence, objects inside the event horizon—including the singularity itself—cannot be directly observed. A naked singularity, by contrast, would be 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 general relativity cannot make predictions about the evolution of
space-time
In physics, spacetime is a mathematical model that combines the three-dimensional space, three dimensions of space and one dimension of time into a single four-dimensional manifold. Minkowski diagram, Spacetime diagrams can be used to visualize S ...
near a singularity. In generic black holes, this is not a problem, as an outside viewer cannot observe the space-time within the event horizon.
Naked singularities have not been observed in nature. Astronomical observations of
black hole
A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
s indicate that their rate of rotation falls below the threshold to produce a naked singularity (spin parameter 1).
GRS 1915+105
GRS 1915+105 or V1487 Aquilae is an X-ray binary star system which features a regular star and a black hole. It was discovered on August 15, 1992 by the WATCH all-sky monitor aboard Granat. "GRS" stands for "GRANAT source", "1915" is the ...
comes closest to the limit, with a spin parameter of 0.82-1.00.
According to the
cosmic censorship hypothesis The weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of gravitational singularities arising in general relativity.
Singularities that arise in the solutions of Einstein's equations are typically ...
, gravitational singularities may not be observable. If
loop quantum gravity
Loop quantum gravity (LQG) is a theory of quantum gravity, which aims to merge quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the pure quantum gravity case. It is an attem ...
is correct, naked singularities may be possible in nature.
Predicted formation
From concepts drawn from
rotating black hole
A rotating black hole is a black hole that possesses angular momentum. In particular, it rotates about one of its axes of symmetry.
All celestial objects – planets, stars (Sun), galaxies, black holes – spin.
Types of black holes
There a ...
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
ergosphere
file:Ergosphere_and_event_horizon_of_a_rotating_black_hole_(no_animation).gif, 300px, In the ergosphere (shown here in light gray), the component ''gtt'' is negative, i.e., acts like a purely spatial metric component. Consequently, timelike or ligh ...
, 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
pulsar
A pulsar (from ''pulsating radio source'') is a highly magnetized rotating neutron star that emits beams of electromagnetic radiation out of its magnetic poles. This radiation can be observed only when a beam of emission is pointing toward Ea ...
s and some computer simulations (
Choptuik, 1997) have been performed.
Mathematician
Demetrios Christodoulou
Demetrios Christodoulou ( el, Δημήτριος Χριστοδούλου; born 19 October 1951) is a Greek mathematician and physicist, who first became well known for his proof, together with Sergiu Klainerman, of the nonlinear stability of the ...
, a winner of the
Shaw Prize
The Shaw Prize is an annual award presented by the Shaw Prize Foundation. Established in 2002 in Hong Kong, it honours "individuals who are currently active in their respective fields and who have recently achieved distinguished and signifi ...
, has shown that contrary to what had been expected, singularities which are not hidden in a black hole also occur. However, he then showed that such "naked singularities" are unstable.
Metrics
![Naked](https://upload.wikimedia.org/wikipedia/commons/4/4b/Naked.Singularity%2COverextremal.Kerr.Newman%2CRaytracing.png)
Disappearing event horizons exist in 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 ge ...
, which is a spinning black hole in a vacuum. Specifically, if the
angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
is high enough, the event horizons could disappear. Transforming the Kerr metric to
Boyer–Lindquist coordinates In the mathematical description of general relativity, the Boyer–Lindquist coordinates are a generalization of the coordinates used for the metric of a Schwarzschild black hole that can be used to express the metric of a Kerr black hole.
The Ha ...
, 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 complex for
, or
. However, this corresponds to a case where
exceeds
(or in
Planck units, , i.e. the spin exceeds what is normally viewed as the upper limit of its physically possible values.
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 horizons occur at
:
where
, and
. Of the three possible cases for the relative values of
and
, the case where
causes both
to be complex. This means the metric is regular for all positive values of
, or in other words, the singularity has no event horizon. However, this corresponds to a case where
exceeds
(or in Planck units, , i.e. the charge exceeds what is normally viewed as the upper limit of its physically possible values.
See
Kerr–Newman metric
The Kerr–Newman metric is the most general asymptotically flat, stationary solution of the Einstein–Maxwell equations in general relativity that describes the spacetime geometry in the region surrounding an electrically charged, rotating mas ...
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 The weak and the strong cosmic censorship hypotheses are two mathematical conjectures about the structure of gravitational singularities arising in general relativity.
Singularities that arise in the solutions of Einstein's equations are typically ...
. Without an event horizon of any kind, some speculate that naked singularities could actually emit light.
Cosmic censorship hypothesis
The cosmic censorship hypothesis says that a gravitational singularity would remain hidden by the event horizon.
LIGO
The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a large-scale physics experiment and observatory designed to detect cosmic gravitational waves and to develop gravitational-wave observations as an astronomical tool. Two large ...
events, including
GW150914
The first direct observation of gravitational waves was made on 14 September 2015 and was announced by the LIGO and Virgo collaborations on 11 February 2016. Previously, gravitational waves had been inferred only indirectly, via their effect on t ...
, are consistent with these predictions. Although data anomalies would have resulted in the case of a singularity, the nature of those anomalies remains unknown.
Some research has suggested that if loop quantum gravity is correct, then naked singularities could exist in nature, implying that the cosmic censorship hypothesis does not hold. Numerical calculations and some other arguments
have also hinted at this possibility.
In fiction
*
M. John Harrison
Michael John Harrison (born 26 July 1945), known for publication purposes primarily as M. John Harrison, is an English author and literary critic.Kelley, George. "Harrison, M(ichael) John" in Jay P. Pederson (.ed) ''St. James guide to sci ...
's
Kefahuchi Tract trilogy of
science fiction
Science fiction (sometimes shortened to Sci-Fi or SF) is a genre of speculative fiction which typically deals with imaginative and futuristic concepts such as advanced science and technology, space exploration, time travel, parallel unive ...
novels (''
Light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
'', ''
Nova Swing
''Nova Swing'' is a science fiction novel by M. John Harrison published in 2006. It takes place in the same universe as ''Light''. The novel won the Arthur C. Clarke and Philip K. Dick Awards in 2007.
Overview
''Nova Swing'' takes place lo ...
'' and ''
Empty Space'') centre upon humanity's exploration of a naked singularity.
* "Dark Peril" by
James C. Glass
James is a common English language surname and given name:
*James (name), the typically masculine first name James
* James (surname), various people with the last name James
James or James City may also refer to:
People
* King James (disambiguat ...
(published in ''
Analog
Analog or analogue may refer to:
Computing and electronics
* Analog signal, in which information is encoded in a continuous variable
** Analog device, an apparatus that operates on analog signals
*** Analog electronics, circuits which use analog ...
'' March 2005), is a story about space travelers on an exploratory mission. While they investigate a strange cosmological phenomenon, their two small space crafts begin to shake, and they are unable to leave the area. One crew member realizes that they are trapped in the
ergosphere
file:Ergosphere_and_event_horizon_of_a_rotating_black_hole_(no_animation).gif, 300px, In the ergosphere (shown here in light gray), the component ''gtt'' is negative, i.e., acts like a purely spatial metric component. Consequently, timelike or ligh ...
of a
black hole
A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
or naked singularity. The story describes a cluster of multiple black holes or singularities, and what the crew does to try to survive this seemingly inescapable situation.
*
Stephen Baxter's
Xeelee Sequence
The Xeelee Sequence (; ) is a series of hard science fiction space opera novels, novellas, and short stories written by British science fiction author Stephen Baxter. The series spans billions of years of fictional history, centering on humanit ...
features the Xeelee, who create a massive ring that produces a naked singularity. It is used to travel to another universe.
* In the episode titled "
Daybreak", the finale of the 2004 reimagined television series
Battlestar Galactica
''Battlestar Galactica'' is an American science fiction media franchise created by Glen A. Larson. The franchise began with the Battlestar Galactica (1978 TV series), original television series in 1978, and was followed by a short-run sequel se ...
, the Cylon colony orbits a naked singularity.
* The Sleeping God in
Peter Hamilton's ''
The Night's Dawn Trilogy
British author Peter F. Hamilton's ''The Night's Dawn Trilogy'' consists of three science fiction novels: '' The Reality Dysfunction'' (1996), ''The Neutronium Alchemist'' (1997), and ''The Naked God'' (1999). A collection of short stories, ' ...
'' is believed to be a naked singularity.
* In
Christopher Nolan
Christopher Edward Nolan (born 30 July 1970) is a British-American filmmaker. Known for his lucrative Cinema of the United States, Hollywood blockbusters with complex storytelling, Nolan is considered a leading filmmaker of the 21st century. ...
's ''
Interstellar'' the nonexistence of a naked singularity hinders humanity from completing a theory of
quantum gravity
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vi ...
due to the inaccessibility of experimental data from inside the
event horizon
In astrophysics, an event horizon is a boundary beyond which events cannot affect an 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 compact obj ...
.
* In the
visual novel
A , often abbreviated as VN, is a form of digital semi-interactive fiction. Visual novels are often associated with and used in the medium of video games, but are not always labeled as such themselves. They combine a textual narrative with sta ...
''
Steins;Gate'', a naked singularity is used to compress the digitalized memories of the protagonist into a smaller size, to then be sent back in time with an improvised "time leap machine".
* In
Vonda McIntyre
Vonda Neel McIntyre () was an American science fiction writer and biologist.
Early life and education
Vonda N. McIntyre was born in Louisville, Kentucky, the daughter of H. Neel and Vonda B. Keith McIntyre, who were born in Poland, Ohio. She ...
's 1981 ''
Star Trek
''Star Trek'' is an American science fiction media franchise created by Gene Roddenberry, which began with the eponymous 1960s television series and quickly became a worldwide pop-culture phenomenon. The franchise has expanded into vari ...
'' novel, ''
The Entropy Effect
''The Entropy Effect'' is a novel by Vonda N. McIntyre set in the fictional '' Star Trek'' Universe. It was originally published in 1981 and is the first original story in Pocket Books' long-running series of Star Trek novels (and the second pub ...
,'' a naked singularity is found to be a side effect of
time travel
Time travel is the concept of movement between certain points in time, analogous to movement between different points in space by an object or a person, typically with the use of a hypothetical device known as a time machine. Time travel is a w ...
experimentation, and threatens to destroy the universe if the time travel experiments are not stopped before they started.
See also
*
Black hole electron
In physics, there is a speculative hypothesis that, if there were a black hole with the same mass, charge and angular momentum as an electron, it would share other properties of the electron. Most notably, Brandon Carter showed in 1968 that the mag ...
*
Gravitational singularity
A gravitational singularity, spacetime singularity or simply singularity is a condition in which gravitational field, gravity is so intense that spacetime itself breaks down catastrophically. As such, a singularity is by definition no longer p ...
*
Ring singularity
A ring singularity or ringularity is the gravitational singularity of a rotating black hole, or a Kerr black hole, that is shaped like a ring.
Description of a ring singularity
When a spherical non-rotating body of a critical radius collapses und ...
References
Further reading
*
* Pankaj S. Joshi
"Do Naked Singularities Break the Rules of Physics?" ''Scientific American'', January 2009.
* Marcus Chown
''New Scientist'', August 2009.
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Black holes