- Kruskal-Szekeres coordinates
general relativityKruskal-Szekeres coordinates, named for Martin Kruskaland George Szekeres, are a coordinate systemfor the Schwarzschild geometryfor a black hole. These coordinates have the advantage that they cover the entire spacetime manifoldof the maximally extended Schwarzschild solution and are well-behaved everywhere outside the physical singularity.
"Conventions": In this article we will take the
metric signatureto be (− + + +) and we will work in units where "c" = 1. The gravitational constant"G" will be kept explicit. We will denote the characteristic mass of the Schwarzschild geometry by "M".
Recall that in
Schwarzschild coordinates, the Schwarzschild metric is given by:,where:is the line element of the 2-sphere
Kruskal-Szekeres coordinates are defined by replacing "t" and "r" by new time and radial coordinates:::for the exterior region , and:::for the interior region
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