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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 ...
(This was the coordinate time and metric that both Eddington and Finkelstein presented in their papers.) This is a plot of the light cones of the v-r coordinates where the r axis is an oblique straight line slanted up to the left. The blue line is an example of one of the v constant lines.
An animation of generating a 30 by 20 maze using Kruskal's algorithm. This algorithm is a randomized version of Kruskal's algorithm. Create a list of all walls, and create a set for each cell, each containing just that one cell. For each wall, in some random order: If the cells divided by this wall belong to distinct sets: Remove the current wall.
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 ]
It is the reverse of Kruskal's algorithm, which is another greedy algorithm to find a minimum spanning tree. Kruskal’s algorithm starts with an empty graph and adds edges while the Reverse-Delete algorithm starts with the original graph and deletes edges from it. The algorithm works as follows: Start with graph G, which contains a list of ...
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 ...
In general relativity conformally flat manifolds can often be used, for example to describe Friedmann–Lemaître–Robertson–Walker metric. [5] However it was also shown that there are no conformally flat slices of the Kerr spacetime. [6] For example, the Kruskal-Szekeres coordinates have line element
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.