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• Penrose–Hawking_singularity_theorems abstract "The Penrose–Hawking singularity theorems are a set of results in general relativity which attempt to answer the question of when gravitation produces singularities.A singularity in solutions of the Einstein field equations is one of two things: a situation where matter is forced to be compressed to a point (a space-like singularity) a situation where certain light rays come from a region with infinite curvature (time-like singularity)Space-like singularities are a feature of non-rotating uncharged black-holes, while time-like singularities are those that occur in charged or rotating black hole exact solutions. Both of them have the following property:geodesic incompleteness. Some light-paths or particle-paths cannot be extended beyond a certain proper-time or affine-parameter (affine parameter is 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 (It does not hold for matter described by a super-field, i.e., the Dirac field). 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.Penrose's theorem is more restricted, it only holds when matter obeys a stronger energy condition, called the dominant energy condition, which means that the energy is bigger than the pressure. All ordinary matter, with the exception of a vacuum expectation value of a scalar field, obeys this condition. During inflation, the universe violates the stronger dominant energy condition (but not the weak energy condition), and inflationary cosmologies avoid the initial big-bang singularity. However, inflationary cosmologies are still past-incomplete, and require physics other than inflation to describe the past boundary of the inflating region of spacetime.Hawking's singularity theorem is for the whole universe, and works backwards in time: in Hawking's original formulation, it guaranteed that the Big Bang has infinite density. Hawking later revised his position in A Brief History of Time (1988) where he stated that \"there was in fact no singularity at the beginning of the universe\" (p50). This revision followed from quantum mechanics, in which general relativity must break down at times less than the Planck time. Hence general relativity cannot be used to show a singularity.It is still an open question whether time-like singularities ever occur in the interior of real charged or rotating black holes, or whether they are artifacts of high symmetry and turn into spacelike singularities when realistic perturbations are added.".
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• Penrose–Hawking_singularity_theorems wikiPageOutDegree "71".
• Penrose–Hawking_singularity_theorems wikiPageRevisionID "696143780".
• Penrose–Hawking_singularity_theorems wikiPageWikiLink A_Brief_History_of_Time.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Angular_momentum.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Big_Bang.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Black_hole.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Category:General_relativity.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Category:Mathematical_methods_in_general_relativity.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Category:Physics_theorems.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Category:Theorems_in_general_relativity.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Cauchy_surface.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Causal_structure.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Centrifugal_force.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Closed_timelike_curve.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Compact_space.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Congruence_(general_relativity).
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Connected_manifold.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Einstein_field_equations.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Einstein–Maxwell–Dirac_equations.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Energy_condition.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Event_horizon.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Fermionic_field.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink General_relativity.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Geodesic.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Geodesically_incomplete.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Geodesics_in_general_relativity.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Globally_hyperbolic_manifold.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Gravitational_singularity.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Inflation_(cosmology).
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Injective_function.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Kerr_metric.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Kerr–Newman_metric.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Manifold.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Myerss_theorem.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink No-hair_theorem.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Planck_time.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Proper_future.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Ray_(optics).
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Raychaudhuri_equation.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Reissner–Nordström_metric.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Ricci_curvature.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Roger_Penrose.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Scalar_field.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Schwarzschild_metric.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Solutions_of_the_Einstein_field_equations.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Spacetime_topology.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Star.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Stephen_Hawking.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Stress–energy_tensor.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Topology.
• Penrose–Hawking_singularity_theorems wikiPageWikiLink Trapped_surface.
• Penrose–Hawking_singularity_theorems wikiPageWikiLinkText "Penrose–Hawking singularity theorems".
• Penrose–Hawking_singularity_theorems wikiPageWikiLinkText "Penrose–Hawking singularity theorems".
• Penrose–Hawking_singularity_theorems wikiPageWikiLinkText "Penrose–Hawking theorems".
• Penrose–Hawking_singularity_theorems wikiPageWikiLinkText "begun as a singularity".
• Penrose–Hawking_singularity_theorems wikiPageWikiLinkText "gravitational singularity theorems".
• Penrose–Hawking_singularity_theorems wikiPageWikiLinkText "singularity theorems".
• Penrose–Hawking_singularity_theorems wikiPageUsesTemplate Template:Arxiv.
• Penrose–Hawking_singularity_theorems wikiPageUsesTemplate Template:Black_holes.
• Penrose–Hawking_singularity_theorems wikiPageUsesTemplate Template:Citation_needed.
• Penrose–Hawking_singularity_theorems wikiPageUsesTemplate Template:Cite_arXiv.
• Penrose–Hawking_singularity_theorems wikiPageUsesTemplate Template:Cite_book.
• Penrose–Hawking_singularity_theorems wikiPageUsesTemplate Template:More_footnotes.
• Penrose–Hawking_singularity_theorems wikiPageUsesTemplate Template:Reflist.
• Penrose–Hawking_singularity_theorems wikiPageUsesTemplate Template:Unreferenced_section.
• Penrose–Hawking_singularity_theorems subject Category:General_relativity.
• Penrose–Hawking_singularity_theorems subject Category:Mathematical_methods_in_general_relativity.
• Penrose–Hawking_singularity_theorems subject Category:Physics_theorems.
• Penrose–Hawking_singularity_theorems subject Category:Theorems_in_general_relativity.
• Penrose–Hawking_singularity_theorems hypernym Set.
• Penrose–Hawking_singularity_theorems type Astrophysic.
• Penrose–Hawking_singularity_theorems type Law.
• Penrose–Hawking_singularity_theorems type Method.
• Penrose–Hawking_singularity_theorems type Object.
• Penrose–Hawking_singularity_theorems type Physic.
• Penrose–Hawking_singularity_theorems type Redirect.
• Penrose–Hawking_singularity_theorems type Theorem.
• Penrose–Hawking_singularity_theorems comment "The Penrose–Hawking singularity theorems are a set of results in general relativity which attempt to answer the question of when gravitation produces singularities.A singularity in solutions of the Einstein field equations is one of two things: a situation where matter is forced to be compressed to a point (a space-like singularity) a situation where certain light rays come from a region with infinite curvature (time-like singularity)Space-like singularities are a feature of non-rotating uncharged black-holes, while time-like singularities are those that occur in charged or rotating black hole exact solutions. ".
• Penrose–Hawking_singularity_theorems label "Penrose–Hawking singularity theorems".
• Penrose–Hawking_singularity_theorems sameAs Q1452678.
• Penrose–Hawking_singularity_theorems sameAs Singularitäten-Theorem.
• Penrose–Hawking_singularity_theorems sameAs قضایای_تکینگی_پنروز-هاوکینگ.
• Penrose–Hawking_singularity_theorems sameAs Théorèmes_sur_les_singularités.
• Penrose–Hawking_singularity_theorems sameAs 特異点定理.
• Penrose–Hawking_singularity_theorems sameAs Teoria_osobliwości_Penrose’a-Hawkinga.
• Penrose–Hawking_singularity_theorems sameAs Teoremas_de_singularidade_Penrose-Hawking.
• Penrose–Hawking_singularity_theorems sameAs m.01r0fg.
• Penrose–Hawking_singularity_theorems sameAs Singularitetssatserna.
• Penrose–Hawking_singularity_theorems sameAs Q1452678.
• Penrose–Hawking_singularity_theorems sameAs 彭罗斯－霍金奇点定理.
• Penrose–Hawking_singularity_theorems wasDerivedFrom Penrose–Hawking_singularity_theorems?oldid=696143780.
• Penrose–Hawking_singularity_theorems isPrimaryTopicOf Penrose–Hawking_singularity_theorems.