
#1
Aug2707, 02:06 AM

P: 1

1. The problem statement, all variables and given/known data
find the transformation that turns this metric: [tex]ds^2=X^2dT^2+dX^2[/tex] into the minkowski metric: diag(1,1). 3. The attempt at a solution attempt 1: I transformed the above metric into the coordinates that use the lines that define the light cone as the axes. Namely, [tex]u=T+ln(X)[/tex] [tex]v=Tln(X)[/tex] attempt 2: If I can transform the above, into the coordinates u and v such that i have [tex] ds^2=dudv [/tex] then I'm done because with another transformation: [tex]dt'=\frac{du+dv}{2}[/tex] [tex]dx'=\frac{dudv}{2}[/tex] I have the relation [tex](dt')^2+dx^2=(\frac{du+dv}{2})^2+(\frac{dudv}{2})^2=dudv.[/tex] Is there a systematic way of doing this? 


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