Subject: Coordinate Transformation Metrics
Date: Fri, 3 Oct 2008 08:38:31 EDT
These are better defined on the following website than in Carroll’s book:
_http://io.uwinnipeg.ca/~vincent/4500.6-001/Cosmology/Black_Holes.htm_ (http://io.uwinnipeg.ca/~vincent/4500.6-001/Cosmology/Black_Holes.htm)
a) Eddington Finkelstein
v = t + r + 2m loge sub e (r / (2m) -1)
ds squared = (1 - 2m / r) dv squared - 2 dv dr - r squared d omega squared
b) Kruskal
u = ( r / (2m) - 1) power half exp (r / (4m)) cosh (t / (4m))
v = ( r /(2m)) - 1) power half exp (r / (4m)) sinh (t / (4m))
ds squared = - (32 m cubed / r) exp ( -2 / (2m)) (du squared - dv squared) - r squared d omega squared
We can again run these through our code.