Editing Penrose–Hawking singularity theorems (section)

== Interpretation and significance ==
In [[general relativity]], a singularity is a place that objects or light rays can reach in a finite time where the curvature becomes infinite, or spacetime stops being a [[manifold]]. Singularities can be found in all the black-hole spacetimes, the [[Schwarzschild metric]], the [[Reissner–Nordström metric]], the [[Kerr metric]] and the [[Kerr–Newman metric]], and in all cosmological solutions that do not have a scalar field energy or a cosmological constant.

One cannot predict what might come "out" of a big-bang singularity in our past, or what happens to an observer that falls "in" to a black-hole singularity in the future, so they require a modification of physical law. Before Penrose, it was conceivable that singularities only form in contrived situations. For example, in the collapse of a [[star]] to form a black hole, if the star is spinning and thus possesses some [[angular momentum]], maybe the [[centrifugal force]] partly counteracts gravity and keeps a singularity from forming. The singularity theorems prove that this cannot happen, and that a singularity will always form once an [[event horizon]] forms.

In the collapsing star example, since all matter and energy is a source of gravitational attraction in general relativity, the additional angular momentum only pulls the star together more strongly as it contracts: the part outside the event horizon eventually settles down to a [[Kerr black hole]] (see [[No-hair theorem]]). The part inside the event horizon necessarily has a singularity somewhere. The proof is somewhat constructive{{snd}}it shows that the singularity can be found by following light-rays from a surface just inside the horizon. But the proof does not say what type of singularity occurs, spacelike, timelike, null, [[orbifold]], jump discontinuity in the metric. It only guarantees that if one follows the time-like geodesics into the future, it is impossible for the boundary of the region they form to be generated by the null geodesics from the surface. This means that the boundary must either come from nowhere or the whole future ends at some finite extension.

An interesting "philosophical" feature of general relativity is revealed by the singularity theorems. Because general relativity predicts the inevitable occurrence of singularities, the theory is not complete without a specification for what happens to matter that hits the singularity. One can extend general relativity
to a unified field theory, such as the [[Einstein–Maxwell–Dirac]] system, where no such singularities occur. {{citation needed|date=February 2025}}