Re: Question for Lubos.
From: Lubos Motl (motl_at_feynman.harvard.edu)
Date: 10/25/04
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Date: Mon, 25 Oct 2004 15:42:14 +0000 (UTC)
On Mon, 25 Oct 2004, Scott wrote:
> I was looking at your paper with Neitzke, hep-th/0301173. I am
> reading 2.4 in the paper and have probably a very basic question. You
> say it is convenient to choose the branch such that n=0. Other than
> convenience, is there some basic reason why this branch is preferred
> over any other branch?
Dear Scott, if I understand your question well, you ask why did we choose
the point r=0, close to our contour, to be mapped to z=0 in the tortoise
coordinate plane.
It's because the number 0 is easy to work with. You can also choose r=0 to
be mapped to z=2.pi.i.n, and the whole argument will be essentially
unchanged. The choice n=0 is not preferred because of any fundamental
reason - it is just a matter of convenience. If you choose a different n,
the only change that you will have to do is to write (z-2.pi.i.n) instead
of z everywhere in the rest of the argument - it is as simple as this
additive shift.
The logarithms in the tortoise coordinate fortunately always appear with a
constant coefficient only - so the convention about the branch is always a
matter of an additive shift, even for more complicated black holes.
Does it answer your question? If I wrote something incorrectly, I believe
that Andy Neitzke will correct me.
All the best,
Lubos
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