Gaussian polar coordinates

In the theory of <a href="/facts/Lorentzian_manifold/VFXsVjqb">Lorentzian manifolds</a>, <a href="/facts/Spherically_symmetric_spacetime/79F30980">spherically symmetric spacetimes</a> admit a family of nested round <a href="/facts/Sphere/4Ivb1cTj">spheres</a>. In each of these spheres, every point can be carried to any other by an appropriate rotation about the centre of symmetry.
There are several different types of coordinate chart that are adapted to this family of nested spheres, each introducing a different kind of distortion. The best known alternative is the <a href="/facts/Schwarzschild_coordinates/N50L86od">Schwarzschild chart</a>, which correctly represents distances within each sphere, but (in general) distorts radial distances and <a href="/facts/Angle/gFUTEQYq">angles</a>. Another popular choice is the <a href="/facts/Isotropic_coordinates/VVpstuNV">isotropic chart</a>, 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 <a href="/facts/Spherically_symmetric_spacetime/79F30980">spherically symmetric spacetime</a> 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.

Gaussian polar coordinates open-in-new

Gaussian polar coordinates