In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. There are several different types of coordinate chart which are adapted to this family of nested spheres; the best known is the Schwarzschild chart, but the isotropic chart is also often useful.
The defining characteristic of an isotropic chart is that its radial coordinate (which is different from the radial coordinate of a Schwarzschild chart) is defined so that light cones appear round. This means that (except in the trivial case of a locally flat manifold), the angular isotropic coordinates do not faithfully represent distances within the nested spheres, nor does the radial coordinate faithfully represent radial distances. On the other hand, angles in the constant time hyperslices are represented without distortion, hence the name of the chart.
Isotropic charts are most often applied to static spherically symmetric spacetimes in metric theories of gravitation such as general relativity, but they can also be used in modeling a spherically pulsating fluid ball, for example. For isolated spherically symmetric solutions of the Einstein field equation, at large distances, the isotropic and Schwarzschild charts become increasingly similar to the usual polar spherical chart on Minkowski spacetime.
and 22 Related for: Isotropic coordinates information
(except in the trivial case of a locally flat manifold), the angular isotropiccoordinates do not faithfully represent distances within the nested spheres...
the direction of an isotropic vector is an isotropic line. IsotropiccoordinatesIsotropiccoordinates are coordinates on an isotropic chart for Lorentzian...
directions. Arthur Eddington gave alternative forms in isotropiccoordinates. For isotropic spherical coordinates r 1 {\displaystyle r_{1}} , θ {\displaystyle \theta...
and we also call them isotropic lines.: 90 In the complex projective plane, points are represented by homogeneous coordinates ( x 1 , x 2 , x 3 ) {\displaystyle...
and pressure equations of a static and spherically symmetric body of isotropic material) Planck length Luminet, J.-P. (1979-05-01). "Image of a spherical...
perfect fluids, isotropiccoordinates, another popular chart for static spherically symmetric spacetimes, Gaussian polar coordinates, a less common alternative...
EMF are obtained using an E-field sensor or H-field sensor which can be isotropic or mono-axial, active or passive. A mono-axial, omnidirectional probe...
Static spherically symmetric perfect fluids Schwarzschild coordinatesIsotropiccoordinates Frame fields in general relativity for more about frame fields...
subspace to a submanifold is co-isotropic (the dual of an isotropic subspace), the submanifold is called co-isotropic. Lagrangian submanifolds of a symplectic...
structure of a static, spherically symmetric relativistic star in isotropiccoordinates: d P d r = − G M ( r ) ρ ( r ) r 2 ( 1 + P ( r ) ρ ( r ) c 2 ) (...
A transversely isotropic material is one with physical properties that are symmetric about an axis that is normal to a plane of isotropy. This transverse...
constant spatial coordinate values to observers who perceive the universe as isotropic. Such observers are called "comoving" observers because they move along...
Hubble parameter H ( t ) = H 0 {\displaystyle H(t)=H_{0}} . In isotropiccoordinates, the McVittie metric is given by d s 2 = − ( 1 − G M 2 c 2 a ( t...
image coordinates can be transformed by means of an arbitrary 2D homography. This includes 2D translations and rotations as well as scaling (isotropic and...
geometry, the circular points at infinity (also called cyclic points or isotropic points) are two special points at infinity in the complex projective plane...
its immediate vicinity clocks are synchronized and light propagates isotropically in space. But the experience when the observers try to synchronize their...
C_{ijkl}=C_{klij}=C_{jikl}=C_{ijlk}} . An elastostatic boundary value problem for an isotropic-homogeneous media is a system of 15 independent equations and equal number...
Schwarzschild coordinates or isotropiccoordinates, 2004: Martin & Visser algorithm, another generating function method which uses Schwarzschild coordinates, 2004:...
being isotropic, that is, there is no property of the space that allows distinguishing between two points or two lines. Therefore, a more isotropic definition...
Schwarzschild coordinatesIsotropiccoordinates, in which light cones are round, and thus useful for studying null dusts. Gaussian polar coordinates, sometimes...
requirement that the stress derives from an elastic energy potential. For isotropic materials, the elasticity tensor has just two independent components,...
Global Information