Editing Naked singularity (section)

==Predicted formation==
When a massive star undergoes a [[gravitational collapse]] due to its own immense gravity, the ultimate outcome of this persistent collapse can manifest as either a black hole or a naked singularity. This holds true across a diverse range of physically plausible scenarios allowed by general relativity. The [[Oppenheimer–Snyder model|Oppenheimer–Snyder–Datt]] (OSD) model illustrates the collapse of a spherical cloud composed of homogeneous dust (pressureless matter).<ref>{{Cite journal |last1=Oppenheimer |first1=J. R. |last2=Snyder |first2=H. |date=1939-09-01 |title=On Continued Gravitational Contraction |journal=Physical Review |volume=56 |issue=5 |pages=455–459 |doi=10.1103/PhysRev.56.455|doi-access=free |bibcode=1939PhRv...56..455O }}</ref><ref>{{Cite journal |last=Datt |first=B. |date=1938-05-01 |title=Über eine Klasse von Lösungen der Gravitationsgleichungen der Relativität |url=https://doi.org/10.1007/BF01374951 |journal=Zeitschrift für Physik |language=de |volume=108 |issue=5 |pages=314–321 |doi=10.1007/BF01374951 |issn=0044-3328|url-access=subscription }}</ref> In this scenario, all the matter converges into the spacetime singularity simultaneously in terms of comoving time. Notably, the event horizon emerges before the singularity, effectively covering it. By allowing an inhomogeneous initial density profile, one can demonstrate a significant alteration in the behavior of the horizon. This leads to two distinct potential outcomes arising from the collapse of generic dust: the formation of a black hole, characterized by the horizon preceding the singularity; or the emergence of a naked singularity, where the horizon is delayed. In the case of a naked singularity, this delay enables null geodesics or [[Ray (optics)|light rays]] to escape the central singularity, where density and curvatures diverge, reaching distant observers.<ref>{{Cite journal |last1=Waugh |first1=B. |last2=Lake |first2=Kayll |date=1988-08-15 |title=Strengths of shell-focusing singularities in marginally bound collapsing self-similar Tolman spacetimes |url=https://link.aps.org/doi/10.1103/PhysRevD.38.1315 |journal=Physical Review D |volume=38 |issue=4 |pages=1315–1316 |doi=10.1103/PhysRevD.38.1315|pmid=9959270 |url-access=subscription }}</ref><ref>{{Cite journal |last1=Waugh |first1=B. |last2=Lake |first2=Kayll |date=1989-09-15 |title=Shell-focusing singularities in spherically symmetric self-similar spacetimes |url=https://link.aps.org/doi/10.1103/PhysRevD.40.2137 |journal=Physical Review D |volume=40 |issue=6 |pages=2137–2139 |doi=10.1103/PhysRevD.40.2137|pmid=10012048 |url-access=subscription }}</ref><ref>{{Cite journal |last1=Joshi |first1=P. S. |last2=Dwivedi |first2=I. H. |date=1993-06-15 |title=Naked singularities in spherically symmetric inhomogeneous Tolman-Bondi dust cloud collapse |url=https://link.aps.org/doi/10.1103/PhysRevD.47.5357 |journal=Physical Review D |volume=47 |issue=12 |pages=5357–5369 |doi=10.1103/PhysRevD.47.5357|pmid=10015558 |arxiv=gr-qc/9303037 }}</ref> In exploring more realistic scenarios of collapse, one avenue involves incorporating pressures into the model. The consideration of gravitational collapse with non-zero pressures and various models including a realistic equation of state, delineating the specific relationship between the density and pressure within the cloud, has been thoroughly examined and investigated by numerous researchers over the years.<ref>Examples include:
*{{Cite journal |last1=Ori |first1=Amos |last2=Piran |first2=Tsvi |date=1987-11-09 |title=Naked singularities in self-similar spherical gravitational collapse |url=http://dx.doi.org/10.1103/physrevlett.59.2137 |journal=Physical Review Letters |volume=59 |issue=19 |pages=2137–2140 |doi=10.1103/physrevlett.59.2137 |pmid=10035434 |issn=0031-9007|url-access=subscription }}
*{{Cite journal |last1=Ori |first1=Amos |last2=Piran |first2=Tsvi |date=1990-08-15 |title=Naked singularities and other features of self-similar general-relativistic gravitational collapse |url=http://dx.doi.org/10.1103/physrevd.42.1068 |journal=Physical Review D |volume=42 |issue=4 |pages=1068–1090 |doi=10.1103/physrevd.42.1068 |pmid=10012941 |issn=0556-2821|url-access=subscription }}
*{{Cite journal |last=Magli |first=Giulio |date=1997-07-01 |title=Gravitational collapse with non-vanishing tangential stresses: a generalization of the Tolman - Bondi model |url=http://dx.doi.org/10.1088/0264-9381/14/7/026 |journal=Classical and Quantum Gravity |volume=14 |issue=7 |pages=1937–1953 |doi=10.1088/0264-9381/14/7/026 |issn=0264-9381|url-access=subscription }}
*{{Cite journal |last=Magli |first=Giulio |date=1998-10-01 |title=Gravitational collapse with non-vanishing tangential stresses: II. A laboratory for cosmic censorship experiments |url=http://dx.doi.org/10.1088/0264-9381/15/10/022 |journal=Classical and Quantum Gravity |volume=15 |issue=10 |pages=3215–3228 |doi=10.1088/0264-9381/15/10/022 |issn=0264-9381|arxiv=gr-qc/9711082 }}
*{{Cite journal |last=Harada |first=Tomohiro |date=1998-10-09 |title=Final fate of the spherically symmetric collapse of a perfect fluid |url=http://dx.doi.org/10.1103/physrevd.58.104015 |journal=Physical Review D |volume=58 |issue=10 |page=104015 |doi=10.1103/physrevd.58.104015 |issn=0556-2821|arxiv=gr-qc/9807038 }}
*{{Cite journal |last1=Harada |first1=Tomohiro |last2=Nakao |first2=Ken-ichi |last3=Iguchi |first3=Hideo |date=1999-07-20 |title=Nakedness and curvature strength of a shell-focusing singularity in spherically symmetric spacetime with vanishing radial pressure |url=http://dx.doi.org/10.1088/0264-9381/16/8/315 |journal=Classical and Quantum Gravity |volume=16 |issue=8 |pages=2785–2796 |doi=10.1088/0264-9381/16/8/315 |issn=0264-9381|arxiv=gr-qc/9904073 }}
*{{Cite journal |last1=Joshi |first1=P. S. |last2=Dwivedi |first2=I. H. |date=January 1999 |title=Initial data and the end state of spherically symmetric gravitational collapse |url=https://dx.doi.org/10.1088/0264-9381/16/1/003 |journal=Classical and Quantum Gravity |language=en |volume=16 |issue=1 |pages=41 |doi=10.1088/0264-9381/16/1/003 |issn=0264-9381|arxiv=gr-qc/9804075 }}
*{{Cite journal |last1=Jhingan |first1=S. |last2=Magli |first2=G. |date=2000-05-09 |title=Black holes versus naked singularities formation in collapsing Einstein clusters |url=http://dx.doi.org/10.1103/physrevd.61.124006 |journal=Physical Review D |volume=61 |issue=12 |page=124006 |doi=10.1103/physrevd.61.124006 |issn=0556-2821|arxiv=gr-qc/9902041 }}
*{{Cite journal |last1=Gonçalves |first1=Sérgio M. C. V. |last2=Jhingan |first2=Sanjay |date=December 2001 |title=Singularities in Gravitational Collapse with Radial Pressure |url=http://dx.doi.org/10.1023/a:1015285531320 |journal=General Relativity and Gravitation |volume=33 |issue=12 |pages=2125–2149 |doi=10.1023/a:1015285531320 |issn=0001-7701|arxiv=gr-qc/0107054 }}
*{{Cite journal |last1=Harada |first1=T. |last2=Iguchi |first2=H. |last3=Nakao |first3=K.-I. |date=2002-03-01 |title=Physical Processes in Naked Singularity Formation |journal=Progress of Theoretical Physics |volume=107 |issue=3 |pages=449–524 |doi=10.1143/ptp.107.449 |issn=0033-068X|doi-access=free |arxiv=gr-qc/0204008 }}
*{{Cite journal |last1=Giambò |first1=Roberto |last2=Giannoni |first2=Fabio |last3=Magli |first3=Giulio |last4=Piccione |first4=Paolo |date=April 2003 |title=New Solutions of Einstein Equations in Spherical Symmetry: The Cosmic Censor to the Court |url=http://dx.doi.org/10.1007/s00220-003-0793-9 |journal=Communications in Mathematical Physics |volume=235 |issue=3 |pages=545–563 |doi=10.1007/s00220-003-0793-9 |issn=0010-3616|arxiv=gr-qc/0204030 }}
*{{Cite journal |last1=Giambò |first1=Roberto |last2=Giannoni |first2=Fabio |last3=Magli |first3=Giulio |last4=Piccione |first4=Paolo |date=June 2004 |title=Naked Singularities Formation in the Gravitational Collapse of Barotropic Spherical Fluids |url=http://dx.doi.org/10.1023/b:gerg.0000022388.11306.e1 |journal=General Relativity and Gravitation |volume=36 |issue=6 |pages=1279–1298 |doi=10.1023/b:gerg.0000022388.11306.e1 |issn=0001-7701|arxiv=gr-qc/0303043 }}</ref> They all result in either a black hole or a naked singularity depending on the initial data.

From concepts drawn from [[rotating black hole]]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]], 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]]s<ref>{{Cite web|last=Crew|first=Bec|title=Naked Singularities Can Actually Exist in a Three-Dimensional Universe, Physicists Predict|url=https://www.sciencealert.com/naked-singularities-can-actually-exist-in-a-three-dimensional-universe-physicists-predict|access-date=2020-09-02|website=ScienceAlert|date=23 May 2017 |language=en-gb}}</ref> and some computer simulations ([[Matthew Choptuik|Choptuik]], 1997) have been performed.<ref>{{cite journal|last1=Garfinkle|first1=David|title=Choptuik scaling and the scale invariance of Einstein's equation|journal=Phys. Rev. D|date=1997|volume=56|issue=6|pages=R3169–R3173|doi=10.1103/PhysRevD.56.R3169|arxiv = gr-qc/9612015 |bibcode = 1997PhRvD..56.3169G }}</ref> Intriguingly, it is recently reported that some spinning [[white dwarfs]] could realistically transmute into rotating naked singularities or [[black holes]] with a wide range of near- and sub-solar-mass values by capturing asymmetric [[dark matter]] particles.<ref>{{cite journal |last1=Chakraborty |first1=C. |last2=Bhattacharyya |first2=S. |date=2024-06-05 |title=Near- and sub-solar-mass naked singularities and black holes from transmutation of white dwarfs|url=https://iopscience.iop.org/article/10.1088/1475-7516/2024/06/007 |journal=Journal of Cosmology and Astroparticle Physics |volume=2024 |issue=6 |pages=007|doi=10.1088/1475-7516/2024/06/007|arxiv=2401.08462 }}</ref> Similarly, spinning [[neutron stars]] could also be transmuted to slowly spinning near–solar-mass naked singularities by capturing asymmetric dark matter particles, if the accumulated cloud of [[dark matter]] particles in the core of a [[neutron star]] can be modeled as an [[Anisotropy|anisotropic]] [[fluid]].<ref>{{cite journal|last1=Chakraborty |first1=C. |last2=Bhattacharyya |first2=S. |last3=Joshi |first3=P. S.|date=2024-07-22 |title=Low mass naked singularities from dark core collapse|url=https://iopscience.iop.org/article/10.1088/1475-7516/2024/07/053 |journal=Journal of Cosmology and Astroparticle Physics |volume=2024 |issue=7 |pages=053|doi=10.1088/1475-7516/2024/07/053|arxiv=2405.08758 }}</ref> In general, the [[precession]] of a [[gyroscope]] and the [[precession]] of orbits of matter falling into a rotating black hole or a naked singularity can be used to distinguish these exotic objects.<ref>{{Cite journal |last1=Chakraborty |first1=C. |last2=Kocherlakota |first2=P. |last3=Joshi |first3=P. S. | date=2017-02-06 |title=Spin precession in a black hole and naked singularity spacetimes |url=https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.044006 |journal=Physical Review D |volume=95 |issue=4 |pages=044006|doi=10.1103/PhysRevD.95.044006|arxiv=1605.00600 }}</ref><ref>{{Cite journal |last1=Chakraborty|first1=C. |last2=Kocherlakota |first2=P. |last3=Patil |first3=M. |last4=Bhattacharyya |first4=S. |last5=Joshi |first5=P. S. |last6=Krolak |first6=A.| date=2017-04-12 |title=Distinguishing Kerr naked singularities and black holes using the spin precession of a test gyro in strong gravitational fields|url=https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084024 |journal=Physical Review D |volume=95 |issue=8 |pages=084024|doi=10.1103/PhysRevD.95.084024|arxiv=1611.08808 }}</ref>

Mathematician [[Demetrios Christodoulou]], a winner of the [[Shaw Prize]], has shown that contrary to what had been expected, singularities which are not hidden in a black hole could also occur.<ref>{{cite journal|author=D.Christodoulou|title=Examples of naked singularity formation in the gravitational collapse of a scalar field|journal=Ann. Math.|volume=140|pages=607–653|year=1994|doi=10.2307/2118619|issue=3|jstor=2118619}}</ref> However, he then showed that such "naked singularities" are unstable.<ref name=instability>{{cite journal|author=D. Christodoulou|title=The instability of naked singularities in the gravitational collapse of a scalar field|journal=Ann. Math.|volume=149|pages=183–217| year=1999|doi=10.2307/121023|issue=1|jstor=121023|arxiv=math/9901147|s2cid=8930550}}</ref>