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Universal coordinates for Schwarzschild black holes
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A variety of historical coordinates in which the Schwarzschild metric is regular over the whole of the extended spacetime are compared and the hypersurfaces of constant coordinate are graphically presented. While the Kruscal form (one of the later forms) is probably the simplest, each of the others has some interesting features.
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Modified Fronsdal coordinates for maximally extended Schwarzschild spacetime
A new 'modified Fronsdal' coordinate system covers the entire maximally extended Schwarzschild spacetime with an explicit areal radius, r = r_s(1 + χ² − η²), at the cost of curved light-cone lines.
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