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The Kruskal–Szekeres coordinates also apply to space-time around a spherical object, but in that case do not give a description of space-time inside the radius of the object. Space-time in a region where a star is collapsing into a black hole is approximated by the Kruskal–Szekeres coordinates (or by the Schwarzschild coordinates). The ...
This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): . The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question.
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.
In practice, the metric of the manifold has to be conformal to the flat metric , i.e., the geodesics maintain in all points of the angles by moving from one to the other, as well as keeping the null geodesics unchanged, [1] that means there exists a function () such that () = (), where () is known as the conformal factor and is a point on the ...
From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Kruskal–Szekeres coordinates
Penrose diagram of an infinite Minkowski universe, horizontal axis u, vertical axis v. In theoretical physics, a Penrose diagram (named after mathematical physicist Roger Penrose) is a two-dimensional diagram capturing the causal relations between different points in spacetime through a conformal treatment of infinity.
The constant tachyonic geodesic outside is not continued by a constant geodesic inside , but rather continues into a "parallel exterior region" (see Kruskal–Szekeres coordinates). Other tachyonic solutions can enter a black hole and re-exit into the parallel exterior region.
Similarly R seems appropriate for an everywhere-spacelike coordinate. Usage in the literature seems mixed. While some use (u,v) others do use (T,R) (t,r) or similar. For example Rindler's Relativity: Special, General and Cosmological uses (t,x). This usage would be similar to the use of (T,X) for Minkowski coordinates in the Rindler coordinates ...