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Statements

Subject Item
dbr:Gaussian_polar_coordinates
rdf:type
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rdfs:label
Gaussian polar coordinates
rdfs:comment
In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. In each of these spheres, every point can be carried to any other by an appropriate rotation about the center of symmetry.
dcterms:subject
dbc:Coordinate_charts_in_general_relativity dbc:Lorentzian_manifolds
dbo:wikiPageID
2934261
dbo:wikiPageRevisionID
1099200679
dbo:wikiPageWikiLink
dbr:Function_(mathematics) dbr:Isotropic_coordinates dbr:Line_element dbr:Spherically_symmetric_spacetime dbr:Static_spacetime dbr:Angle dbr:Lorentzian_manifold dbr:Spacetime_metric dbr:Sphere dbr:Schwarzschild_coordinates dbc:Coordinate_charts_in_general_relativity dbr:Frame_fields_in_general_relativity dbr:Static_spherically_symmetric_perfect_fluid dbc:Lorentzian_manifolds
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yes
dbp:date
December 2009
dbo:abstract
In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. In each of these spheres, every point can be carried to any other by an appropriate rotation about the center of symmetry. There are several different types of coordinate chart which are adapted to this family of nested spheres, each introducing a different kind of distortion. The best known alternative is the Schwarzschild chart, which correctly represents distances within each sphere, but (in general) distorts radial distances and angles. Another popular choice is the isotropic chart, which correctly represents angles (but in general distorts both radial and transverse distances). A third choice is the Gaussian polar chart, which correctly represents radial distances, but distorts transverse distances and angles. There are other possible charts; the article on spherically symmetric spacetime describes a coordinate system with intuitively appealing features for studying infalling matter. In all cases, the nested geometric spheres are represented by coordinate spheres, so we can say that their roundness is correctly represented.
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