Naked singularity

In general relativity, a naked singularity is a gravitational singularity without an event horizon. In a black hole, the singularity is completely enclosed by a boundary known as the event horizon, inside which the gravitational force of 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, 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 general relativity cannot make predictions about the future evolution of space-time 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.

Some research has suggested that if loop quantum gravity is correct, then naked singularities could exist in nature,^[1]^[2]^[3] implying that the cosmic censorship hypothesis does not hold. Numerical calculations^[4] and some other arguments^[5] have also hinted at this possibility.

At LIGO, first observation of gravitational waves were detected after the collision two black holes, known as event GW150914. This event did not produce a naked singularity based on observation.^[6]

Predicted formation

From concepts drawn from rotating black holes, 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, 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 pulsars and some computer simulations (Choptuik, 1997) have been performed.^[7]

This is 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 gravity should be able to solve problems such as these.

Shaw Prize winning mathematician Demetrios Christodoulou has shown that contrary to what had been expected, singularities which are not hidden in a black hole also occur.^[8] However, he then showed that such "naked singularities" are unstable.^[9]

Metrics

Disappearing event horizons exist in the Kerr metric, which is a spinning black hole in a vacuum. Specifically, if the angular momentum is high enough, the event horizons could disappear. Transforming the Kerr metric to Boyer–Lindquist coordinates, it can be shown^[10] that the $r$ coordinate (which is not the radius) of the event horizon is

$r_{\pm }=\mu \pm (\mu ^{2}-a^{2})^{1/2}$ ,

where $\mu =GM/c^{2}$ , and $a=J/Mc$ . In this case, "event horizons disappear" means when the solutions are complex for $r_{\pm }$ , or $\mu ^{2}<a^{2}$ .

Disappearing event horizons can also be seen with the Reissner–Nordström geometry of a charged black hole. In this metric, it can be shown^[11] that the singularities occur at

$r_{\pm }=\mu \pm (\mu ^{2}-q^{2})^{1/2}$ ,

where $\mu =GM/c^{2}$ , and $q^{2}=GQ^{2}/(4\pi \epsilon _{0}c^{4})$ . Of the three possible cases for the relative values of $\mu$ and $q$ , the case where $\mu ^{2}<q^{2}$ causes both $r_{\pm }$ to be complex. This means the metric is regular for all positive values of $r$ , or in other words, the singularity has no event horizon.

See Kerr–Newman metric 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.^[12]

Cosmic censorship hypothesis

The cosmic censorship hypothesis says that a naked singularity cannot arise in our universe from realistic initial conditions.

In fiction

M. John Harrison's Kefahuchi Tract trilogy of science fiction novels (Light, Nova Swing and Empty Space) centre upon humanity's exploration of a naked singularity.
"Dark Peril" by James C. Glass (published in 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 of a black hole 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 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, the Cylon colony orbits a naked singularity.
The Sleeping God in Peter Hamilton's The Night's Dawn Trilogy is believed to be a naked singularity.
In Christopher Nolan's Interstellar the nonexistence of a naked singularity hinders humanity from completing a theory of quantum gravity due to the inaccessibility of experimental data from inside the event horizon.

References

↑ M. Bojowald, Living Rev. Rel. 8, (2005), 11
↑ R. Goswami & P. Joshi, Phys. Rev. D, (2008)
↑ R. Goswami, P. Joshi, & P. Singh, Phys. Rev. Letters, (2006), 96
↑ D. Eardley & L. Smarr, Phys. Rev. D., (1979), 19
↑ A. Krolak, Prog. Theor. Phys. Supp., (1999) 136, 45
↑ https://physics.aps.org/articles/v9/52
↑ Garfinkle, David (1997). "Choptuik scaling and the scale invariance of Einstein's equation". Phys. Rev. D. 56 (6). Bibcode:1997PhRvD..56.3169G. arXiv:gr-qc/9612015 . doi:10.1103/PhysRevD.56.R3169.
↑ D.Christodoulou (1994). "Examples of naked singularity formation in the gravitational collapse of a scalar field". Ann. Math. 140 (3): 607–653. doi:10.2307/2118619.
↑ D. Christodoulou (1999). "The instability of naked singularities in the gravitational collapse of a scalar field". Ann. Math. 149 (1): 183–217. doi:10.2307/121023.
↑ Hobson, et al., General Relativity an Introduction for Physicists, Cambridge University Press 2007, p. 300-305
↑ Hobson, et al., General Relativity an Introduction for Physicists, Cambridge University Press 2007, p. 320-325
↑ Stephen Battersby (1 October 2007). "Is a 'naked singularity' lurking in our galaxy?". New Scientist. Retrieved 2008-03-06.

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.

Black holes
Types	Schwarzschild Rotating Charged Virtual Binary
Size	Micro Extremal Electron Stellar Intermediate-mass Supermassive Quasar Active galactic nucleus Blazar Large quasar group
Formation	Stellar evolution Gravitational collapse Neutron star Related links Compact star Quark Exotic Tolman–Oppenheimer–Volkoff limit White dwarf Related links Supernova Related links Hypernova Gamma-ray burst
Properties	Thermodynamics Schwarzschild radius M–sigma relation Event horizon Quasi-periodic oscillation Photon sphere Ergosphere Hawking radiation Penrose process Blandford–Znajek process Bondi accretion Spaghettification Gravitational lens
Models	Gravitational singularity Penrose–Hawking singularity theorems Primordial black hole Gravastar Dark star Dark-energy star Black star Eternally collapsing object Magnetospheric eternally collapsing object Fuzzball White hole Naked singularity Ring singularity Immirzi parameter Membrane paradigm Kugelblitz Wormhole Quasi-star
Issues	No-hair theorem Information paradox Cosmic censorship Alternative models Holographic principle Black hole complementarity firewall (physics) ER=EPR Final parsec problem
Metrics	Schwarzschild Kerr Reissner–Nordström Kerr–Newman
Lists	Black holes Most massive Quasars
Related	Timeline of black hole physics Rossi X-ray Timing Explorer Hypercompact stellar system Gamma-ray burst progenitors Gravity well Black hole starship

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