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Physics
Special and General Relativity
Invariance of timelike Killing vector of Schwarzschild sol.
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[QUOTE="TomServo, post: 6130008, member: 253819"] I wasn't exact enough with my question about invariance. I know that invariance of a scalar field refers to the invariance of the value of that scalar at that point in spacetime. What I see by plotting r vs. ##\rho## is that for ##0<\rho<\infty## we never go below ##2m##. It dips to the point where ##r=2m## as ##\rho\rightarrow \frac{m}{2}## but for ##\rho<\frac{m}{2}## it goes to infinity. IOW it seems like the portion of the manifold covered by ##0<r<2m## isn't present in the isotropic coordinates, so points on the inside of the event horizon are not covered by ##\rho<\frac{m}{2}## in isotropic coordinates like I thought they were, but rather those points (##\rho<\frac{m}{2}##) correspond to...something else? Thanks for your help. [/QUOTE]
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Physics
Special and General Relativity
Invariance of timelike Killing vector of Schwarzschild sol.
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