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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 ...
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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.
In these coordinate systems, outward (inward) traveling radial light rays (which each follow a null geodesic) define the surfaces of constant "time", while the radial coordinate is the usual area coordinate so that the surfaces of rotation symmetry have an area of 4 π r 2.
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.
Fields that are now often introduced with coordinate-free treatments include vector calculus, tensors, differential geometry, and computer graphics. [2] In physics, the existence of coordinate-free treatments of physical theories is a corollary of the principle of general covariance.
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Kruskal's algorithm [1] finds a minimum spanning forest of an undirected edge-weighted graph. If the graph is connected , it finds a minimum spanning tree . It is a greedy algorithm that in each step adds to the forest the lowest-weight edge that will not form a cycle . [ 2 ]