Editing Gravitational collapse (section)

===Black holes===
{{Main|Black hole}}
[[File:MassDensi.jpg|thumb|400px|Logarithmic plot of mass against mean density (with solar values as origin) showing possible kinds of stellar equilibrium state. For a configuration in the shaded region, beyond the black hole limit line, no equilibrium is possible, so runaway collapse will be inevitable.]]
According to Einstein's theory, for even larger stars, above the Landau–Oppenheimer–Volkoff limit, also known as the [[Tolman–Oppenheimer–Volkoff limit]] (roughly double the mass of the Sun) no known form of cold matter can provide the force needed to oppose gravity in a new dynamical equilibrium. Hence, the collapse continues with nothing to stop it.  [[file:CNRSblackhole.jpg|thumb|250px|left|Simulated view from outside black hole with thin accretion disc<ref>{{cite journal | last=Marck | first=Jean-Alain | title=Short-cut method of solution of geodesic equations for Schwarzchild black hole | journal=Classical and Quantum Gravity | volume=13 | issue=3 | date=1996-03-01 | issn=0264-9381 | doi=10.1088/0264-9381/13/3/007 | pages=393–402| arxiv=gr-qc/9505010 | bibcode=1996CQGra..13..393M | s2cid=119508131 }}</ref>]]  
Once a body collapses to within its [[Schwarzschild radius]] it forms what is called a black hole, meaning a spacetime region from which not even light can escape. It follows from [[general relativity]] and the theorem of [[Roger Penrose]]<ref>{{cite journal | last=Penrose | first=Roger | title=Gravitational Collapse and Space–Time Singularities | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=14 | issue=3 | date=1965-01-18 | issn=0031-9007 | doi=10.1103/physrevlett.14.57 | pages=57–59| bibcode=1965PhRvL..14...57P | doi-access=free }}</ref> that the subsequent formation of some kind of [[gravitational singularity|singularity]] is inevitable. Nevertheless, according to Penrose's [[cosmic censorship hypothesis]], the singularity will be confined within the event horizon bounding the black hole, so the spacetime region outside will still have a well-behaved geometry, with strong but finite curvature, that is expected<ref>{{cite journal | last=Carter | first=B. | title=Axisymmetric Black Hole Has Only Two Degrees of Freedom | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=26 | issue=6 | date=1971-02-08 | issn=0031-9007 | doi=10.1103/physrevlett.26.331 | pages=331–333| bibcode=1971PhRvL..26..331C }}</ref> to evolve towards a rather simple form describable by the historic [[Schwarzschild metric]] in the spherical limit and by the more recently discovered [[Kerr metric]] if angular momentum is present. If the precursor has a magnetic field, it is dispelled during the collapse, as black holes are thought to have no magnetic field of their own.<ref>{{cite journal |last1=Baumgarte |first1=Thomas W. |last2=Shapiro |first2=Stuart L. |title=Collapse of a Magnetized Star to a Black Hole |journal=The Astrophysical Journal |date=10 March 2003 |volume=585 |issue=2 |pages=930–947 |doi=10.1086/346104  |arxiv=astro-ph/0211339 |bibcode=2003ApJ...585..930B |s2cid=15869680 }}</ref>

On the other hand, the nature of the kind of singularity to be expected inside a black hole remains rather controversial. According to theories based on [[quantum mechanics]], at a later stage, the collapsing object will reach the maximum possible energy density for a certain volume of space or the [[Planck density]] (as there is nothing that can stop it). This is the point at which it has been hypothesized that the known laws of gravity cease to be valid.<ref>{{cite conference |last=Thorne |first=Kip S. |date=1966 |title=The general-relativistic theory of stellar structure and dynamics |url=https://www.its.caltech.edu/~kip/index.html/PubScans/II-12.pdf |conference=Proceedings of the International School of Physics “Enrico Fermi”, Course XXXV |editor=L. Gratton |location=Varenna, Italy |publisher=Academic Press, New York |pages=273 |language=en}}</ref> There are competing theories as to what occurs at this point. For example [[loop quantum gravity]] predicts that a [[Planck star]] would form. Regardless, it is argued that gravitational collapse ceases at that stage and a singularity, therefore, does not form.<ref>{{Cite journal |last1=Rovelli |first1=Carlo |last2=Vidotto |first2=Francesca |date=2014 |title=Planck stars |url=https://www.worldscientific.com/doi/abs/10.1142/S0218271814420267 |journal=[[International Journal of Modern Physics D]] |language=en |volume=23 |issue=12 |pages=1442026 |doi=10.1142/S0218271814420267 |issn=0218-2718|arxiv=1401.6562 |bibcode=2014IJMPD..2342026R |s2cid=118917980 }}</ref>

====Theoretical minimum radius for a star====

The radii of larger mass neutron stars (about 2.8 solar mass)<ref>{{Cite web | url=https://ejje.weblio.jp/content/Bhatia+Hazarika+limit |title = Bhatia Hazarika limitの意味・使い方・読み方 &#124; Weblio英和辞書}}</ref>  are estimated to be about 12&nbsp;km, or approximately 2 times their equivalent Schwarzschild radius.

It might be thought that a sufficiently massive neutron star could exist within its Schwarzschild radius (1.0 SR) and appear like a black hole without having all the mass compressed to a singularity at the center; however, this is probably incorrect. Within the [[event horizon]], the matter would have to move outward faster than the speed of light in order to remain stable and avoid collapsing to the center. No physical force, therefore, can prevent a star smaller than 1.0 SR from collapsing to a singularity (at least within the currently accepted framework of [[general relativity]]; this does not hold for the Einstein–Yang–Mills–Dirac system). A model for the nonspherical collapse in general relativity with the emission of matter and [[gravitational waves]] has been presented.<ref>{{cite journal |last1=Bedran |first1=M. L. |last2=Calvão |first2=M. O. |last3=de Oliveira |first3=H. P. |last4=Damião |first4=I. |date=1996 |title=Model for nonspherical collapse and formation of black holes by the emission of neutrinos, strings and gravitational waves |journal=Physical Review D |volume=54 |issue=6 |pages=3826–3829 |doi=10.1103/PhysRevD.54.3826|pmid=10021057 |bibcode=1996PhRvD..54.3826B |url=https://cds.cern.ch/record/301262 }}</ref>