# Ring singularity

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Gravitational singularity of a rotating black hole

A **ring singularity** or **ringularity** is the [gravitational singularity](/source/Gravitational_singularity) of a [rotating](/source/Rotating_black_hole) [black hole](/source/Black_hole), or a [Kerr black hole](/source/Kerr_black_hole), that is shaped like a ring.[1]

## Description

Event horizons and ergospheres of a rotating black hole; the ringularity is located at the equatorial kink of the inner ergosphere at R=a.

When a spherical non-rotating body of a critical radius collapses under its own [gravitation](/source/Gravitation) under [general relativity](/source/General_relativity), theory suggests it will collapse to a 0-dimensional single point. This is not the case with a rotating black hole (a [Kerr black hole](/source/Kerr_black_hole)). With a fluid rotating body, its distribution of mass is not [spherical](/source/Spherical) (it shows an [equatorial bulge](/source/Equatorial_bulge)), and it has [angular momentum](/source/Angular_momentum). Since a point cannot support [rotation](/source/Rotation) or [angular momentum](/source/Angular_momentum) in [classical physics](/source/Classical_physics) (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](/source/Frame-dragging) effects, described by the [Kerr metric](/source/Kerr_metric), 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](/source/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](/source/Event_horizon) of a non-rotating and uncharged black hole (a [Schwarzschild black hole](/source/Schwarzschild_black_hole)) cannot avoid the central singularity, which lies in the future [world line](/source/World_line) of everything within the horizon. Thus, one cannot avoid [spaghettification](/source/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. This makes it theoretically (but not likely practically)[2] possible for the Kerr black hole to act as a sort of [wormhole](/source/Wormhole), possibly even a traversable wormhole.[3]

## 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](/source/Bernoulli's_principle). (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](/source/Penrose%E2%80%93Hawking_singularity_theorems) under general relativity involves arbitrarily dense conditions, [quantum effects](/source/Quantum_mechanics) 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.[4] This observation was supported by the investigation of charged black holes which exhibited similar "infinite blueshifting" behavior.[5] 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.[6][7][8][9][10]

## See also

- [Black hole](/source/Black_hole)

- [Black hole electron](/source/Black_hole_electron)

- [Gravitational singularity](/source/Gravitational_singularity)

- [Geon (physics)](/source/Geon_(physics))

## Further reading

- [Thorne, Kip](/source/Kip_Thorne) (1995). [*Black Holes and Time Warps: Einstein's Outrageous Legacy*](/source/Black_Holes_and_Time_Warps). New York: [W. W. Norton & Company](/source/W._W._Norton_%26_Company). [ISBN](/source/ISBN_(identifier)) [978-0-393-31276-8](https://en.wikipedia.org/wiki/Special:BookSources/978-0-393-31276-8).

- [Visser, Matt](/source/Matt_Visser) (1995). *Lorentzian Wormholes: From Einstein to Hawking*. Woodbury: [American Institute of Physics](/source/American_Institute_of_Physics). [ISBN](/source/ISBN_(identifier)) [978-1-56396-394-0](https://en.wikipedia.org/wiki/Special:BookSources/978-1-56396-394-0).

## References

1. **[^](#cite_ref-1)** Sukys, Paul (1999). [*Lifting the Scientific Veil*](https://archive.org/details/liftingscientifi0000suky/page/533). Oxford: [Rowman & Littlefield](/source/Rowman_%26_Littlefield). p. [533](https://archive.org/details/liftingscientifi0000suky/page/533). [ISBN](/source/ISBN_(identifier)) [978-0-8476-9600-0](https://en.wikipedia.org/wiki/Special:BookSources/978-0-8476-9600-0).

1. **[^](#cite_ref-kerrtube_2-0)** Roy Kerr: *[Spinning Black Holes](https://www.youtube.com/watch?v=nypav68tq8Q&t=48m5s)* (Lecture at the University of Canterbury, timecode [49m8s](https://www.youtube.com/watch?v=nypav68tq8Q&t=49m8s)

1. **[^](#cite_ref-3)** Kaufmann, William J. III (1977). [*The Cosmic Frontiers of General Relativity*](https://archive.org/details/cosmicfrontierso00unse). Boston, Toronto: [Little, Brown and Company](/source/Little%2C_Brown_and_Company). p. 178,9. [ISBN](/source/ISBN_(identifier)) [978-0-316-48341-4](https://en.wikipedia.org/wiki/Special:BookSources/978-0-316-48341-4).

1. **[^](#cite_ref-Penrose1_4-0)** Penrose, R. (1968). de Witt, C.; Wheeler, J. (eds.). *Battelle Rencontres*. New York: [W. A. Benjamin](/source/W._A._Benjamin). p. 222.

1. **[^](#cite_ref-Penrose2_5-0)** Poisson, E.; Israel, W. (1990). "Internal structure of black holes". *Phys. Rev. D*. **41** (6): 1796–1809. [Bibcode](/source/Bibcode_(identifier)):[1990PhRvD..41.1796P](https://ui.adsabs.harvard.edu/abs/1990PhRvD..41.1796P). [doi](/source/Doi_(identifier)):[10.1103/PhysRevD.41.1796](https://doi.org/10.1103%2FPhysRevD.41.1796). [PMID](/source/PMID_(identifier)) [10012548](https://pubmed.ncbi.nlm.nih.gov/10012548).

1. **[^](#cite_ref-6)** Hod, Shahar; Tsvi Piran (1998). "The Inner Structure of Black Holes". *Gen. Rel. Grav*. **30** (11): 1555. [arXiv](/source/ArXiv_(identifier)):[gr-qc/9902008](https://arxiv.org/abs/gr-qc/9902008). [Bibcode](/source/Bibcode_(identifier)):[1998GReGr..30.1555H](https://ui.adsabs.harvard.edu/abs/1998GReGr..30.1555H). [doi](/source/Doi_(identifier)):[10.1023/A:1026654519980](https://doi.org/10.1023%2FA%3A1026654519980). [S2CID](/source/S2CID_(identifier)) [7001639](https://api.semanticscholar.org/CorpusID:7001639).

1. **[^](#cite_ref-7)** Ori, Amos (1999). "Oscillatory Null Singularity inside Realistic Spinning Black Holes". *[Physical Review Letters](/source/Physical_Review_Letters)*. **83** (26): 5423–5426. [arXiv](/source/ArXiv_(identifier)):[gr-qc/0103012](https://arxiv.org/abs/gr-qc/0103012). [Bibcode](/source/Bibcode_(identifier)):[1999PhRvL..83.5423O](https://ui.adsabs.harvard.edu/abs/1999PhRvL..83.5423O). [doi](/source/Doi_(identifier)):[10.1103/PhysRevLett.83.5423](https://doi.org/10.1103%2FPhysRevLett.83.5423). [S2CID](/source/S2CID_(identifier)) [15112314](https://api.semanticscholar.org/CorpusID:15112314).

1. **[^](#cite_ref-8)** Brady, Patrick R; Serge Droz; Sharon M Morsink (1998). "The late-time singularity inside non-spherical black holes". *Physical Review D*. **58** (8) 084034. [arXiv](/source/ArXiv_(identifier)):[gr-qc/9805008](https://arxiv.org/abs/gr-qc/9805008). [Bibcode](/source/Bibcode_(identifier)):[1998PhRvD..58h4034B](https://ui.adsabs.harvard.edu/abs/1998PhRvD..58h4034B). [doi](/source/Doi_(identifier)):[10.1103/PhysRevD.58.084034](https://doi.org/10.1103%2FPhysRevD.58.084034). [S2CID](/source/S2CID_(identifier)) [118307468](https://api.semanticscholar.org/CorpusID:118307468).

1. **[^](#cite_ref-9)** Novikov, Igor D. (2003). *Developments in General Relativity: Black Hole Singularity and Beyond*. Texas in Tuscany. Xxi Symposium on Relativistic Astrophysics. *Texas in Tuscany*. pp. 77–90. [arXiv](/source/ArXiv_(identifier)):[gr-qc/0304052](https://arxiv.org/abs/gr-qc/0304052). [Bibcode](/source/Bibcode_(identifier)):[2003tsra.symp...77N](https://ui.adsabs.harvard.edu/abs/2003tsra.symp...77N). [doi](/source/Doi_(identifier)):[10.1142/9789812704009_0008](https://doi.org/10.1142%2F9789812704009_0008). [ISBN](/source/ISBN_(identifier)) [978-981-238-580-2](https://en.wikipedia.org/wiki/Special:BookSources/978-981-238-580-2). [S2CID](/source/S2CID_(identifier)) [17200476](https://api.semanticscholar.org/CorpusID:17200476).

1. **[^](#cite_ref-10)** Burko, Lior M.; Amos Ori (1995-02-13). "Are physical objects necessarily burnt up by the blue sheet inside a black hole?". *[Physical Review Letters](/source/Physical_Review_Letters)*. **74** (7): 1064–1066. [arXiv](/source/ArXiv_(identifier)):[gr-qc/9501003](https://arxiv.org/abs/gr-qc/9501003). [Bibcode](/source/Bibcode_(identifier)):[1995PhRvL..74.1064B](https://ui.adsabs.harvard.edu/abs/1995PhRvL..74.1064B). [doi](/source/Doi_(identifier)):[10.1103/PhysRevLett.74.1064](https://doi.org/10.1103%2FPhysRevLett.74.1064). [PMID](/source/PMID_(identifier)) [10058925](https://pubmed.ncbi.nlm.nih.gov/10058925). [S2CID](/source/S2CID_(identifier)) [13887924](https://api.semanticscholar.org/CorpusID:13887924).

v t e Black holes Outline Types BTZ black hole Schwarzschild Rotating Charged Virtual Kugelblitz Supermassive Primordial Direct collapse Rogue Malament–Hogarth spacetime Size Micro Extremal Electron Stellar Microquasar Intermediate-mass Supermassive Active galactic nucleus Quasar LQG Blazar BL Lac FSRQ Formation Stellar evolution Gravitational collapse Neutron star Related links Tolman–Oppenheimer–Volkoff limit Oppenheimer–Snyder model White dwarf Related links Supernova Micronova Hypernova Related links Gamma-ray burst Binary black hole Quark star Supermassive star Quasi-star Supermassive dark star X-ray binary Properties Astrophysical jet Gravitational singularity Ring singularity BKL singularity Shock singularity Theorems Event horizon Photon sphere Innermost stable circular orbit Ergosphere Penrose process Blandford–Znajek process Accretion disk Hawking radiation Gravitational lens Microlens Cauchy horizon Mass inflation Bondi accretion M–sigma relation Quasi-periodic oscillation Thermodynamics Bekenstein bound Bousso's holographic bound Immirzi parameter Schwarzschild radius Spaghettification Issues Information paradox Complementarity Soft hair Cosmic censorship ER = EPR Final parsec problem Firewall (physics) Holographic principle No-hair theorem Metrics Schwarzschild (Derivation) Kerr Reissner–Nordström Kerr–Newman Hayward Alternatives Nonsingular black hole models Black star Dark star Dark-energy star Gravastar Magnetospheric eternally collapsing object Planck star Q star Fuzzball Geon Analogs Optical black hole Sonic black hole Lists Black holes Most massive Nearest Quasars Microquasars Related Outline of black holes Black Hole Initiative Black hole starship Black holes in fiction Big Bang Big Bounce Compact star Exotic star Quark star Preon star Gravitational waves Gamma-ray burst progenitors Gravity well Hypercompact stellar system Membrane paradigm Naked singularity Population III star Supermassive star Quasi-star Supermassive dark star Rossi X-ray Timing Explorer Superluminal motion Timeline of black hole physics White hole Wormhole Tidal disruption event Notable 1ES 1927+654 3C 273 A0620-00 AT2018hyz Centaurus A Cygnus X-1 Gaia BH1 Hercules A Markarian 501 MS 0735.6+7421 NeVe 1 OJ 287 Phoenix Cluster PKS 1302-102 PSO J030947.49+271757.31 Q0906+6930 Sagittarius A* SDSS J0849+1114 Swift J1644+57 TON 618 ULAS J1342+0928 XTE J1118+480 XTE J1650-500 Category Commons

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