Hi Scott,
On Wed, Oct 06, 2010 at 12:18:11PM -0400, Scott Noble wrote:
I see that this has not been patched yet. Can someone please confirm the fix and patch the repo?
Thanks for submitting the patch and for helping understanding the problem. I just committed the patch of the code (and the documentation). I also added the lines of sagemath I used to proof that the patch is actually correct, and I attach this here for the record.
Frank
This document shows that the denominator of the definition of shift_phi in the code (p2*Sigma) is equal to the denominator of equation (11) in Phys. Rev., D54, 14031416
Lines starting with '>' are commands for sagemath, line starting with
are sagemath output, everything else is comments.
Variable definition:
Sigma,a,r,m,R,Delta,st2,ct2=var('Sigma,a,r,m,R,Delta,st2,ct2')
This is p2*Sigma from the code, st2 being sin^2(theta) = rho^2/R^2:
code_denom=(a^2+r^2)*Sigma+2*m*a^2*r*st2
Now substitute Sigma, with ct2 being cos^2(theta) = z^2/R^2:
code_denom=code_denom.substitute(Sigma=r^2+a^2*ct2)
and use that st2+ct2=1:
code_denom=code_denom.substitute(ct2=1-st2)
Now look at the denominator in the paper:
paper_denom=(r^2+a^2)^2-a^2*st2*Delta
Substitute Delta:
paper_denom=paper_denom.substitute(Delta=r^2-2*m*r+a^2)
And look at the difference between code_denom and paper_denom:
(code_denom-paper_denom).expand()
0
qed
And here is the notebook as textblock:
sage: Sigma,a,r,m,R,Delta,st2,ct2=var('Sigma,a,r,m,R,Delta,st2,ct2') sage: code_denom=(a^2+r^2)*Sigma+2*m*a^2*r*st2 sage: code_denom=code_denom.substitute(Sigma=r^2+a^2*ct2) sage: code_denom=code_denom.substitute(ct2=1-st2) sage: paper_denom=(r^2+a^2)^2-a^2*st2*Delta sage: paper_denom=paper_denom.substitute(Delta=r^2-2*m*r+a^2) sage: (code_denom-paper_denom).expand() 0