Editing General relativity (section)

=== Singularities ===
{{Main|Spacetime singularity}}
Another general feature of general relativity is the appearance of spacetime boundaries known as singularities. Spacetime can be explored by following up on timelike and lightlike geodesics—all possible ways that light and particles in free fall can travel. But some solutions of Einstein's equations have "ragged edges"—regions known as [[spacetime singularity|spacetime singularities]], where the paths of light and falling particles come to an abrupt end, and geometry becomes ill-defined. In the more interesting cases, these are "curvature singularities", where geometrical quantities characterizing spacetime curvature, such as the [[Ricci scalar]], take on infinite values.<ref>{{Harvnb|Hawking|Ellis|1973|loc=sec. 8.1}}, {{Harvnb|Wald|1984|loc=sec. 9.1}}</ref> Well-known examples of spacetimes with future singularities—where worldlines end—are the Schwarzschild solution, which describes a singularity inside an eternal static black hole,<ref>{{Harvnb|Townsend|1997|loc=ch. 2}}; a more extensive treatment of this solution can be found in {{Harvnb|Chandrasekhar|1983|loc=ch. 3}}</ref> or the Kerr solution with its ring-shaped singularity inside an eternal rotating black hole.<ref>{{Harvnb|Townsend|1997|loc=ch. 4}}; for a more extensive treatment, cf. {{Harvnb|Chandrasekhar|1983|loc=ch. 6}}</ref> The Friedmann–Lemaître–Robertson–Walker solutions and other spacetimes describing universes have past singularities on which worldlines begin, namely Big Bang singularities, and some have future singularities ([[Big Crunch]]) as well.<ref>{{Harvnb|Ellis|Van Elst|1999}}; a closer look at the singularity itself is taken in {{Harvnb|Börner|1993|loc=sec. 1.2}}</ref>

Given that these examples are all highly symmetric—and thus simplified—it is tempting to conclude that the occurrence of singularities is an artifact of idealization.<ref>Here one should remind to the well-known fact that the important "quasi-optical" singularities of the so-called [[eikonal approximation]]s of many wave equations, namely the "[[caustic (mathematics)|caustics]]", are resolved into finite peaks beyond that approximation.</ref> The famous [[singularity theorems]], proved using the methods of global geometry, say otherwise: singularities are a generic feature of general relativity, and unavoidable once the collapse of an object with realistic matter properties has proceeded beyond a certain stage<ref>Namely when there are [[trapped null surface]]s, cf. {{Harvnb|Penrose|1965}}</ref> and also at the beginning of a wide class of expanding universes.<ref>{{Harvnb|Hawking|1966}}</ref> However, the theorems say little about the properties of singularities, and much of current research is devoted to characterizing these entities' generic structure (hypothesized e.g. by the [[BKL singularity|BKL conjecture]]).<ref>The conjecture was made in {{Harvnb|Belinskii|Khalatnikov|Lifschitz|1971}}; for a more recent review, see {{Harvnb|Berger|2002}}. An accessible exposition is given by {{Harvnb|Garfinkle|2007}}</ref> The [[cosmic censorship hypothesis]] states that all realistic future singularities (no perfect symmetries, matter with realistic properties) are safely hidden away behind a horizon, and thus invisible to all distant observers. While no formal proof yet exists, numerical simulations offer supporting evidence of its validity.<ref>The restriction to future singularities naturally excludes initial singularities such as the big bang singularity, which in principle be visible to observers at later cosmic time. The cosmic censorship conjecture was first presented in {{Harvnb|Penrose|1969}}; a textbook-level account is given in {{Harvnb|Wald|1984|pp=302–305}}. For numerical results, see the review {{Harvnb|Berger|2002|loc=sec. 2.1}}</ref>