About: Schwarzschild coordinates

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In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. In such a spacetime, a particularly important kind of coordinate chart is the Schwarzschild chart, a kind of polar spherical coordinate chart on a static and spherically symmetric spacetime, which is adapted to these nested round spheres. The defining characteristic of Schwarzschild chart is that the radial coordinate possesses a natural geometric interpretation in terms of the surface area and Gaussian curvature of each sphere. However, radial distances and angles are not accurately represented.

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rdfs:label	Singularité de Schwarzschild (fr) Schwarzschild coordinates (en)
rdfs:comment	In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. In such a spacetime, a particularly important kind of coordinate chart is the Schwarzschild chart, a kind of polar spherical coordinate chart on a static and spherically symmetric spacetime, which is adapted to these nested round spheres. The defining characteristic of Schwarzschild chart is that the radial coordinate possesses a natural geometric interpretation in terms of the surface area and Gaussian curvature of each sphere. However, radial distances and angles are not accurately represented. (en) La singularité de Schwarzschild est le comportement divergent de la métrique de Schwarzschild quand . Il ne faut pas la confondre avec la singularité gravitationnelle d'un trou noir. Cette singularité n'est qu'apparente : elle se manifeste dans l'expression classique de cette métrique, mais pas dans d'autres. On considère donc que c'est une singularité mathématique pour la métrique classique de Schwarzschild, mais que ce n'est pas une singularité physique. Différents changements de notations ont été proposés pour le montrer, par exemple les coordonnées de Lemaître ou de Kruskal-Szekeres. Une autre démarche est possible avec les coordonnées isotropes, présentant des avantages et des inconvénients. (fr)
dcterms:subject	Lorentzian manifolds Coordinate charts in general relativity
Wikipage page ID	30862736 (xsd:integer)
Wikipage revision ID	987944726 (xsd:integer)
Link from a Wikipage to another Wikipage	Pressure Proper time Schwarzschild metric Topogravitic tensor Coordinate chart Bel decomposition Black hole Deriving the Schwarzschild solution Ansatz Proper length World line Gaussian polar coordinates Einstein field equation Energy conditions Gaussian curvature General relativity Boyer–Lindquist coordinates Congruence (general relativity) Traceless Annulus (mathematics) Lie algebra Lorentzian manifold Stress–energy tensor Kruskal–Szekeres coordinates Static spacetime Line element Locus (mathematics) Perfect fluid Eddington–Finkelstein coordinates Euclidean space Frame fields in general relativity Isotropic coordinates Killing vector field Lorentzian manifolds Kerr metric Birkhoff's theorem (relativity) Electrogravitic tensor Coordinate charts in general relativity Spacetime Spherical coordinates Metric theory of gravitation Integral Metric tensor Surface area Gullstrand–Painlevé coordinates Event horizon Static spherically symmetric perfect fluid Spherically symmetric spacetime Magnetogravitic tensor Riemann tensor Cartan formalism Reissner–Nordström black hole Connection one-form Coframe fields in general relativity Spacelike vector Vorticity tensor dbr:Bach_bar dbr:Lorentzian_adjoint dbr:Reissner–Nordström–de_Sitter dbr:Space_time_metric
sameAs	Schwarzschild coordinates Schwarzschild coordinates Schwarzschild coordinates Schwarzschild coordinates Schwarzschild coordinates
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has abstract	La singularité de Schwarzschild est le comportement divergent de la métrique de Schwarzschild quand . Il ne faut pas la confondre avec la singularité gravitationnelle d'un trou noir. Cette singularité n'est qu'apparente : elle se manifeste dans l'expression classique de cette métrique, mais pas dans d'autres. On considère donc que c'est une singularité mathématique pour la métrique classique de Schwarzschild, mais que ce n'est pas une singularité physique. Différents changements de notations ont été proposés pour le montrer, par exemple les coordonnées de Lemaître ou de Kruskal-Szekeres. Une autre démarche est possible avec les coordonnées isotropes, présentant des avantages et des inconvénients. Par contre, certaines propriété physiques qui s'y manifestent font qu'on nomme cette région de l'espace horizon de Schwarzschild ou horizon des événements. Avec les coordonnées de Lemaître ou de Kruskal-Szekeres, on conclut à l'existence d'un effondrement du trou noir en une singularité centrale (pour ). (fr) In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. In such a spacetime, a particularly important kind of coordinate chart is the Schwarzschild chart, a kind of polar spherical coordinate chart on a static and spherically symmetric spacetime, which is adapted to these nested round spheres. The defining characteristic of Schwarzschild chart is that the radial coordinate possesses a natural geometric interpretation in terms of the surface area and Gaussian curvature of each sphere. However, radial distances and angles are not accurately represented. These charts have many applications in metric theories of gravitation such as general relativity. They are most often used in static spherically symmetric spacetimes. In the case of general relativity, Birkhoff's theorem states that every isolated spherically symmetric vacuum or electrovacuum solution of the Einstein field equation is static, but this is certainly not true for perfect fluids. The extension of the exterior region of the Schwarzschild vacuum solution inside the event horizon of a spherically symmetric black hole is not static inside the horizon, and the family of (spacelike) nested spheres cannot be extended inside the horizon, so the Schwarzschild chart for this solution necessarily breaks down at the horizon. (en)
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foaf:isPrimaryTopicOf	wikipedia-en:Schwarzschild_coordinates
is Link from a Wikipage to another Wikipage of	Schwarzschild metric Black hole Rindler coordinates Index of physics articles (S) Analytic continuation Gaussian polar coordinates Construction of a complex null tetrad Coordinate system

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