Editing Penrose–Hawking singularity theorems (section)

== Singularity ==
A singularity in [[solutions of the Einstein field equations]] is one of three things:

* Spacelike singularities: The singularity lies in the future or past of all events within a certain region. The Big Bang singularity and the typical singularity inside a non-rotating, uncharged [[Schwarzschild metric|Schwarzschild black hole]] are spacelike.
* Timelike singularities: These are singularities that can be avoided by an observer because they are not necessarily in the future of all events. An observer might be able to move around a timelike singularity. These are less common in known solutions of the [[Einstein field equations]].
* Null singularities: These singularities occur on light-like or null surfaces. An example might be found in certain types of black hole interiors, such as the [[Cauchy horizon]] of a charged ([[Reissner–Nordström metric|Reissner–Nordström]]) or rotating ([[Kerr metric|Kerr]]) black hole.

A singularity can be either strong or weak:

* Weak singularities: A weak singularity is one where the tidal forces (which are responsible for the [[spaghettification]] in black holes) are not necessarily infinite. An observer falling into a weak singularity might not be torn apart before reaching the singularity, although the laws of physics would still break down there. The Cauchy horizon inside a charged or rotating black hole might be an example of a weak singularity.
* Strong singularities: A strong singularity is one where tidal forces become infinite. In a strong singularity, any object would be destroyed by infinite tidal forces as it approaches the singularity. The singularity at the center of a Schwarzschild black hole is an example of a strong singularity.

Space-like singularities are a feature of non-rotating uncharged [[black hole]]s as described by the [[Schwarzschild metric]], while time-like singularities are those that occur in charged or rotating black hole exact solutions. Both of them have the property of [[Geodesic manifold|geodesic incompleteness]], in which either some light-path or some particle-path cannot be extended beyond a certain proper time or affine parameter (affine parameter being the null analog of proper time).

The Penrose theorem guarantees that some sort of geodesic incompleteness occurs inside ''any'' black hole whenever matter satisfies reasonable [[energy conditions]]. The energy condition required for the black-hole singularity theorem is weak: it says that light rays are always focused together by gravity, never drawn apart, and this holds whenever the energy of matter is non-negative.

Hawking's singularity theorem is for the whole universe, and works backwards in time: it guarantees that the (classical) [[Big Bang]] has infinite density.<ref>{{cite web|last1=Hawking|first1=Stephen|title=Properties of expanding universes|url=https://cudl.lib.cam.ac.uk/view/MS-PHD-05437/115|website=Cambridge Digital Library|access-date=24 October 2017}}</ref> This theorem is more restricted and only holds when matter obeys a stronger energy condition, called the ''[[energy condition#strong energy condition|strong energy condition]]'', in which the energy is larger than the pressure. All ordinary matter, with the exception of a vacuum expectation value of a [[scalar field]], obeys this condition. During [[Cosmic inflation|inflation]], the universe violates the dominant energy condition, and it was initially argued (e.g. by Starobinsky<ref>{{Cite journal |first=Alexei A. |last=Starobinsky |title=A new type of isotropic cosmological models without singularity |journal=Physics Letters B |volume=91 |issue=1 |pages=99&ndash;102 |date=1980 |bibcode=1980PhLB...91...99S |doi=10.1016/0370-2693(80)90670-X}}</ref>) that inflationary cosmologies could avoid the initial big-bang singularity. However, it has since been shown that inflationary cosmologies are still past-incomplete,<ref>{{Cite journal|title = Inflationary spacetimes are not past-complete|journal = Physical Review Letters|date = 2003-04-15|issn = 0031-9007|volume = 90|issue = 15|doi = 10.1103/PhysRevLett.90.151301|first1 = Arvind|last1 = Borde|first2 = Alan H.|last2 = Guth|first3 = Alexander|last3 = Vilenkin|arxiv = gr-qc/0110012 |bibcode = 2003PhRvL..90o1301B|pmid=12732026|pages=151301|s2cid = 46902994}}</ref> and thus require physics other than inflation to describe the past boundary of the inflating region of spacetime.

It is still an open question whether (classical) general relativity predicts spacelike singularities in the interior of realistic charged or rotating black holes, or whether these are artefacts of high-symmetry solutions and turn into null or timelike singularities when perturbations are added.{{citation needed|date=February 2025}}