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The transformation between Schwarzschild coordinates and Kruskal–Szekeres coordinates defined for r > 2GM and < < can be extended, as an analytic function, at least to the first singularity which occurs at =. Thus the above metric is a solution of Einstein's equations throughout this region.
An example is the apparent (longitudinal) singularity at the 90 degree latitude in spherical coordinates. An object moving due north (for example, along the line 0 degrees longitude ) on the surface of a sphere will suddenly experience an instantaneous change in longitude at the pole (i.e., jumping from longitude 0 to longitude 180 degrees).
Kruskal–Szekeres coordinates, a chart covering the entire spacetime manifold of the maximally extended Schwarzschild solution and are well-behaved everywhere outside the physical singularity, Eddington–Finkelstein coordinates, an alternative chart for static spherically symmetric spacetimes,
The metric in Kruskal–Szekeres coordinates covers all of the extended Schwarzschild spacetime in a single coordinate system. Its chief disadvantage is that in those coordinates the metric depends on both the time and space coordinates.
As the article correctly says the "curvature singularity is given by the equation UV = 1". Thus one of U or V may be varied freely (with the other determined thereby) while remaining at the singularity. Thus three dimensions have either been constrained or rendered null while one dimension remains. In other words, the singularity is one ...
Liberal netizens tore into Sen. Deb Fischer's (R-Neb.) elderly husband Bruce for appearing to turn down Vice President Kamala Harris' handshake last week, but viral footage that swirled online ...
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Image credits: Ok-File-6997 Animal shelters in the US had a busy 2023, with over 6.5 million pets entering shelters and rescue organizations. That’s 3.3 million cats and 3.2 million dogs. It was ...