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In general relativity, Kruskal–Szekeres coordinates, named after Martin Kruskal and George Szekeres, are a coordinate system for the Schwarzschild geometry for a black hole. These coordinates have the advantage that they cover the entire spacetime manifold of the maximally extended Schwarzschild solution and are well-behaved everywhere ...
Eddington–Finkelstein coordinates are founded upon the tortoise coordinate – a name that comes from one of Zeno of Elea's paradoxes on an imaginary footrace between "swift-footed" Achilles and a tortoise. The tortoise coordinate is defined: = + | |.
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.
Gullstrand–Painlevé coordinates are a particular set of coordinates for the Schwarzschild metric – a solution to the Einstein field equations which describes a black hole. The ingoing coordinates are such that the time coordinate follows the proper time of a free-falling observer who starts from far away at zero velocity, and the spatial ...
Working in a coordinate chart with coordinates (,,,) labelled 1 to 4 respectively, we begin with the metric in its most general form (10 independent components, each of which is a smooth function of 4 variables). The solution is assumed to be spherically symmetric, static and vacuum.
An R-square of 0.6 is considered the minimum acceptable level. [citation needed] An R-square of 0.8 is considered good for metric scaling and .9 is considered good for non-metric scaling. Other possible tests are Kruskal’s Stress, split data tests, data stability tests (i.e., eliminating one brand), and test-retest reliability.