[Users] [Fwd: Kerr ID]

[Erik Schnetter]

On Wed, Oct 6, 2010 at 8:45 PM, Scott Noble <scn at astro.rit.edu> wrote:
>
> Hello Erik and Bruno,
>
>  I do not know off-hand a place in the literature where \beta^\phi is
> stated.  \beta^\phi in BL coordinates is rarely expressed since the BL
> metric is usually given in line element form, not in ADM form.
>
>  It should be simple enough to derive it from the other components, which
> (IMHO) are correct.   I could make a maple script that derives it, but then
> you'd have to trust that I wrote up the maple script correctly...

Either we trust you, or you could commit the Maple script (in ASCII
form so that it is easily readable) to the documentation.

>  FYI: I believe
>
>  shift_phi = \beta^\phi    and
>  beta_phi = \beta_\phi    .

Yes, that makes sense! I was puzzled about that difference and didn't
think of a lowered index.

> -- scott n.
>
>
> On 10/6/10 8:29 PM, Bruno Coutinho Mundim wrote:
>>
>> Hi Scott and Erik,
>>
>> I was also looking into this issue now. The mapping from the PRD 54 1403
>> paper to the code documentation seems to go as in:
>>
>> Paper Documentation
>> r r_k
>> \bar{r} r
>> quasi-isotropic radius \eta ???
>>
>> Also note that the Sigma definition in the documentation is not the
>> usual definition in Boyer-Lindquist coordinates.
>>
>> I hope there is a reference for the documentation. Otherwise, the
>> non-usual notation there prevents us of a simple check.
>>
>> Thanks,
>> Bruno.
>>
>> Erik Schnetter wrote:
>>>
>>> Scott
>>>
>>> Do you have a pointer to literature that contains the correct
>>> equation? I'm looking at PRD 54 1403, which is the paper cited in the
>>> thorn; is that a good choice? Do you know how the variables in the
>>> paper are mapped to the variables in the code? The code documentation
>>> (the latex file doc/documentation.tex) seems consistent with the C
>>> code, but of course both could be wrong. Or is there an easy way to
>>> see why the factor Sigma is missing?
>>>
>>> I haven't used the Boyer-Lindquist Kerr initial data implemented in
>>> this thorn myself; I usually use Kerr-Schild coordinates form thorn
>>> Exact.
>>>
>>> -erik
>>>
>>> On Wed, Oct 6, 2010 at 11:18 AM, Scott Noble <scn at astro.rit.edu> wrote:
>>>>
>>>> I see that this has not been patched yet. Can someone please confirm the
>>>> fix and
>>>> patch the repo?
>>>>
>>>> thanks, scott n.
>>>>
>>>>
>>>> -------- Original Message --------
>>>> Subject: Kerr ID
>>>> Date: Mon, 07 Jun 2010 16:54:20 -0400
>>>> From: Scott Noble <scn at astro.rit.edu>
>>>> To: users at einsteintoolkit.org
>>>>
>>>>
>>>> Hello Users,
>>>>
>>>>
>>>> I believe I found a minor typo in
>>>>
>>>> EinsteinInitialData/IDAnalyticBH/src/Kerr.c
>>>>
>>>> of the ET. Just a missing term in the denominator of the shift
>>>> vector, so
>>>> it will not likely affect many users. I have attached a patch.
>>>>
>>>> cheers,
>>>>
>>>> -- scott n.
>>>>
>>>>
>>>>
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>>>>
>>>>
>>>
>>>
>>>
>>
>



-- 
Erik Schnetter <schnetter at cct.lsu.edu>   http://www.cct.lsu.edu/~eschnett/