Editing General relativity (section)

=== Horizons ===
{{Main|Horizon (general relativity)|No hair theorem|Black hole mechanics}}
Using global geometry, some spacetimes can be shown to contain boundaries called [[event horizon|horizons]], which demarcate one region from the rest of spacetime. The best-known examples are black holes: if mass is compressed into a sufficiently compact region of space (as specified in the [[hoop conjecture]], the relevant length scale is the [[Schwarzschild radius]]<ref>{{Harvnb|Thorne|1972}}; for more recent numerical studies, see {{Harvnb|Berger|2002|loc=sec. 2.1}}</ref>), no light from inside can escape to the outside. Since no object can overtake a light pulse, all interior matter is imprisoned as well. Passage from the exterior to the interior is still possible, showing that the boundary, the black hole's ''horizon'', is not a physical barrier.<ref>{{Harvnb|Israel|1987}}. A more exact mathematical description distinguishes several kinds of horizon, notably event horizons and [[apparent horizon]]s cf. {{Harvnb|Hawking|Ellis|1973|pp=312–320}} or {{Harvnb|Wald|1984|loc=sec. 12.2}}; there are also more intuitive definitions for isolated systems that do not require knowledge of spacetime properties at infinity, cf. {{Harvnb|Ashtekar|Krishnan|2004}}</ref>

[[File:Ergosphere of a rotating black hole.svg|thumb|The ergosphere of a rotating black hole, which plays a key role when it comes to extracting energy from such a black hole]]
Early studies of black holes relied on explicit solutions of Einstein's equations, notably the spherically symmetric Schwarzschild solution (used to describe a [[Static spacetime|static]] black hole) and the axisymmetric [[Kerr solution]] (used to describe a rotating, [[Stationary spacetime|stationary]] black hole, and introducing interesting features such as the ergosphere). Using global geometry, later studies have revealed more general properties of black holes. With time they become rather simple objects characterized by eleven parameters specifying: electric charge, mass–energy, [[linear momentum]], [[angular momentum]], and location at a specified time. This is stated by the [[no hair theorem|black hole uniqueness theorem]]: "black holes have no hair", that is, no distinguishing marks like the hairstyles of humans. Irrespective of the complexity of a gravitating object collapsing to form a black hole, the object that results (having emitted gravitational waves) is very simple.<ref>For first steps, cf. {{Harvnb|Israel|1971}}; see {{Harvnb|Hawking|Ellis|1973|loc=sec. 9.3}} or {{Harvnb|Heusler|1996|loc=ch. 9 and 10}} for a derivation, and {{Harvnb|Heusler|1998}} as well as {{Harvnb|Beig|Chruściel|2006}} as overviews of more recent results</ref>

Even more remarkably, there is a general set of laws known as [[black hole mechanics]], which is analogous to the [[laws of thermodynamics]]. For instance, by the second law of black hole mechanics, the area of the event horizon of a general black hole will never decrease with time, analogous to the [[entropy]] of a thermodynamic system. This limits the energy that can be extracted by classical means from a rotating black hole (e.g. by the [[Penrose process]]).<ref>The laws of black hole mechanics were first described in {{Harvnb|Bardeen|Carter|Hawking|1973}}; a more pedagogical presentation can be found in {{Harvnb|Carter|1979}}; for a more recent review, see {{Harvnb|Wald|2001|loc=ch. 2}}. A thorough, book-length introduction including an introduction to the necessary mathematics {{Harvnb|Poisson|2004}}. For the Penrose process, see {{Harvnb|Penrose|1969}}</ref> There is strong evidence that the laws of black hole mechanics are, in fact, a subset of the laws of thermodynamics, and that the black hole area is proportional to its entropy.<ref>{{Harvnb|Bekenstein|1973}}, {{Harvnb|Bekenstein|1974}}</ref> This leads to a modification of the original laws of black hole mechanics: for instance, as the second law of black hole mechanics becomes part of the second law of thermodynamics, it is possible for the black hole area to decrease as long as other processes ensure that entropy increases overall. As thermodynamical objects with nonzero temperature, black holes should emit [[thermal radiation]]. Semiclassical calculations indicate that indeed they do, with the surface gravity playing the role of temperature in [[Planck's law]]. This radiation is known as [[Hawking radiation]] (cf. the [[#Quantum field theory in curved spacetime|quantum theory section]], below).<ref>The fact that black holes radiate, quantum mechanically, was first derived in {{Harvnb|Hawking|1975}}; a more thorough derivation can be found in {{Harvnb|Wald|1975}}. A review is given in {{Harvnb|Wald|2001|loc=ch. 3}}</ref>

There are many other types of horizons. In an expanding universe, an observer may find that some regions of the past cannot be observed ("[[particle horizon]]"), and some regions of the future cannot be influenced (event horizon).<ref>{{Harvnb|Narlikar|1993|loc=sec. 4.4.4, 4.4.5}}</ref> Even in flat Minkowski space, when described by an accelerated observer ([[Rindler space]]), there will be horizons associated with a semiclassical radiation known as [[Unruh effect|Unruh radiation]].<ref>Horizons: cf. {{Harvnb|Rindler|2001|loc=sec. 12.4}}. Unruh effect: {{Harvnb|Unruh|1976}}, cf. {{Harvnb|Wald|2001|loc=ch. 3}}</ref>