U and V in the Kruskal Diagram

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SUMMARY

The variables u and v in the Kruskal diagram are indeed functions of the time coordinate t. The transformation from Schwarzschild coordinates to Kruskal coordinates is defined by the equations u = -4M e^{-u/4M} and v = 4M e^{v/4M}, where u = t - r* and v = t + r*. Here, r* is given by the formula r* = r + 2M ln|(r/2M) - 1|. This confirms the relationship between these coordinates in the context of general relativity.

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I would just like to verify whether or not the variables u and v in the Kruskal diagram are functions of t. Thanks!
 
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The transformation from Schwarzschild coordinates r, t to Kruskal coordinates u and v is:

u = -4M e-u/4M
v = 4M ev/4M

where u = t - r*, v = t + r*, and r* = r + 2M ln|(r/2M) -1|
 
ok, that clears things up, thanks!
 

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