Re: [Users] QuasiLocalMeasures BH Spin

[Eloisa Bentivegna]

On 02/03/17 15:35, Roland Haas wrote:
> Hello Eloisa, Gwyneth, Erik,
> 
>> as you've noticed, QLM implements various measures of a surface spin
>> (some better tested than others). Unfortunately the references to the
>> corresponding formalisms are scattered around, but here's a primer:
> This information seems to be missing from the thorn documentation.
> Would it be possible to add it (even the primer that Eliosa provided)
> to it? Either directly for those that have commit rights or as a pull
> request on bitbucket?

Hi Roland,

there is a bibliography in QuasiLocalMeasures/README, which is
essentially equivalent to what I said. Do you think we should annotate
it further?

Eloisa
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Re: [Users] QuasiLocalMeasures BH Spin

[Gwyneth Allwright]

Thanks for the help Eloisa and Vassili! I really appreciate it.

Gwyneth


On Thu, Mar 2, 2017 at 6:51 PM, Vassilios Mewes 
wrote:

> Hello Gwyneth and Eloisa,
>
> On Thu, Mar 2, 2017 at 8:31 AM, Eloisa Bentivegna <
> eloisa.bentive...@ct.infn.it> wrote:
>
>> On 28/02/17 09:43, Gwyneth Allwright wrote:
>> > Hi All,
>> >
>> > I'm trying to reproduce the testbed BBH results in Etienne et al. 2009:
>> > https://arxiv.org/abs/0812.2245
>> >
>> > I'd like to calculate the final Kerr black hole spin using the ratio of
>> > the polar and equatorial circumferences. QuasiLocalMeasures qlm_scalars
>> > gives several spin-related quantities:
>> >
>> > qlm_spin_guess
>> > qlm_spin
>> > qlm_npspin
>> > qlm_wsspin
>> > qlm_cvspin
>> > qlm_coordspinx, qlm_coordspiny and qlm_coordspinz.
>> >
>> > How are these related? Are any of them calculated using the Kerr
>> formula?
>>
>> Dear Gwyneth,
>>
>> as you've noticed, QLM implements various measures of a surface spin
>> (some better tested than others). Unfortunately the references to the
>> corresponding formalisms are scattered around, but here's a primer:
>>
>> 1) qlm_spin_guess is a spin estimate which assumes the spacetime is
>> Kerr, and uses the area and equatorial circumference of the surface to
>> build the spin according to
>>
>> ! equatorial circumference L, area A
>>
>> ! L = 2 pi (r^2 + a^2) / r
>> ! A = 4 pi (r^2 + a^2)
>> ! r = M + sqrt (M^2 - a^2)
>>
>> ! r = A / (2 L)
>> ! a^2 = A / (4 pi) - r^2   ("spin" a = J/M = specific angular momentum)
>> ! M = (r^2 + a^2) / (2 r)
>>
>> ! J = a M   (angular momentum)
>>
>> (this is from the thorn's qlm_analyse.F90)
>>
>> If the assumption is fine with you, you can just use this estimate.
>>
>> 2) qlm_spin is equation (25) in http://arxiv.org/pdf/gr-qc/0206008.pdf
>> (in a nutshell, it involves identifying a rotational symmetry on the
>> surface and constructing the corresponding conserved charge);
>>
>> 3) qlm_npspin and qlm_wsspin are measures of angular momentum based on
>> the Newman-Penrose coefficients and Weyl scalars, respectively (for an
>> example of what the integrands look like on e.g. Kerr, you can take a
>> look at Chapter 6 of Chandrasekhar's book);
>>
>> 4) qlm_cvspin is, as far as I can tell, currently not set;
>>
>> 5) qlm_coordspin* is the same as 2), but assuming that the generators of
>> the rotational symmetry are the x, y, and z axis, respectively.
>>
>
> Just to add, this measure is identical to the angular momentum calculated
> using the Weinberg pseudotensor in qlm_analyse.f90 (as the calculations are
> performed with the lapse =1 and shift =0 in the thorn). In case of an
> axisymmetric horizon, this is equal to to the Komar angular momentum of the
> BH (https://arxiv.org/pdf/1505.07225.pdf).
>
>>
>> > Also: what's the difference between qlm_polar_circumference_0 and
>> > qlm_polar_circumference_pi_2?
>>
>> These are the length of the meridians at phi=0 and phi=pi/2, respectively.
>>
>> Best,
>> Eloisa
>>
>
> Best wishes,
>
> Vassili
>
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Re: [Users] QuasiLocalMeasures BH Spin

[Vassilios Mewes]

Hello Gwyneth and Eloisa,

On Thu, Mar 2, 2017 at 8:31 AM, Eloisa Bentivegna <
eloisa.bentive...@ct.infn.it> wrote:

> On 28/02/17 09:43, Gwyneth Allwright wrote:
> > Hi All,
> >
> > I'm trying to reproduce the testbed BBH results in Etienne et al. 2009:
> > https://arxiv.org/abs/0812.2245
> >
> > I'd like to calculate the final Kerr black hole spin using the ratio of
> > the polar and equatorial circumferences. QuasiLocalMeasures qlm_scalars
> > gives several spin-related quantities:
> >
> > qlm_spin_guess
> > qlm_spin
> > qlm_npspin
> > qlm_wsspin
> > qlm_cvspin
> > qlm_coordspinx, qlm_coordspiny and qlm_coordspinz.
> >
> > How are these related? Are any of them calculated using the Kerr formula?
>
> Dear Gwyneth,
>
> as you've noticed, QLM implements various measures of a surface spin
> (some better tested than others). Unfortunately the references to the
> corresponding formalisms are scattered around, but here's a primer:
>
> 1) qlm_spin_guess is a spin estimate which assumes the spacetime is
> Kerr, and uses the area and equatorial circumference of the surface to
> build the spin according to
>
> ! equatorial circumference L, area A
>
> ! L = 2 pi (r^2 + a^2) / r
> ! A = 4 pi (r^2 + a^2)
> ! r = M + sqrt (M^2 - a^2)
>
> ! r = A / (2 L)
> ! a^2 = A / (4 pi) - r^2   ("spin" a = J/M = specific angular momentum)
> ! M = (r^2 + a^2) / (2 r)
>
> ! J = a M   (angular momentum)
>
> (this is from the thorn's qlm_analyse.F90)
>
> If the assumption is fine with you, you can just use this estimate.
>
> 2) qlm_spin is equation (25) in http://arxiv.org/pdf/gr-qc/0206008.pdf
> (in a nutshell, it involves identifying a rotational symmetry on the
> surface and constructing the corresponding conserved charge);
>
> 3) qlm_npspin and qlm_wsspin are measures of angular momentum based on
> the Newman-Penrose coefficients and Weyl scalars, respectively (for an
> example of what the integrands look like on e.g. Kerr, you can take a
> look at Chapter 6 of Chandrasekhar's book);
>
> 4) qlm_cvspin is, as far as I can tell, currently not set;
>
> 5) qlm_coordspin* is the same as 2), but assuming that the generators of
> the rotational symmetry are the x, y, and z axis, respectively.
>

Just to add, this measure is identical to the angular momentum calculated
using the Weinberg pseudotensor in qlm_analyse.f90 (as the calculations are
performed with the lapse =1 and shift =0 in the thorn). In case of an
axisymmetric horizon, this is equal to to the Komar angular momentum of the
BH (https://arxiv.org/pdf/1505.07225.pdf).

>
> > Also: what's the difference between qlm_polar_circumference_0 and
> > qlm_polar_circumference_pi_2?
>
> These are the length of the meridians at phi=0 and phi=pi/2, respectively.
>
> Best,
> Eloisa
>

Best wishes,

Vassili

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Re: [Users] QuasiLocalMeasures BH Spin

[Roland Haas]

Hello Eloisa, Gwyneth, Erik,

> as you've noticed, QLM implements various measures of a surface spin
> (some better tested than others). Unfortunately the references to the
> corresponding formalisms are scattered around, but here's a primer:
This information seems to be missing from the thorn documentation.
Would it be possible to add it (even the primer that Eliosa provided)
to it? Either directly for those that have commit rights or as a pull
request on bitbucket?

Yours,
Roland

-- 
My email is as private as my paper mail. I therefore support encrypting
and signing email messages. Get my PGP key from http://keys.gnupg.net.


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Re: [Users] QuasiLocalMeasures BH Spin

[Eloisa Bentivegna]

On 28/02/17 09:43, Gwyneth Allwright wrote:
> Hi All,
> 
> I'm trying to reproduce the testbed BBH results in Etienne et al. 2009:
> https://arxiv.org/abs/0812.2245
> 
> I'd like to calculate the final Kerr black hole spin using the ratio of
> the polar and equatorial circumferences. QuasiLocalMeasures qlm_scalars
> gives several spin-related quantities:
> 
> qlm_spin_guess
> qlm_spin
> qlm_npspin
> qlm_wsspin
> qlm_cvspin
> qlm_coordspinx, qlm_coordspiny and qlm_coordspinz.
> 
> How are these related? Are any of them calculated using the Kerr formula?

Dear Gwyneth,

as you've noticed, QLM implements various measures of a surface spin
(some better tested than others). Unfortunately the references to the
corresponding formalisms are scattered around, but here's a primer:

1) qlm_spin_guess is a spin estimate which assumes the spacetime is
Kerr, and uses the area and equatorial circumference of the surface to
build the spin according to

! equatorial circumference L, area A

! L = 2 pi (r^2 + a^2) / r
! A = 4 pi (r^2 + a^2)
! r = M + sqrt (M^2 - a^2)

! r = A / (2 L)
! a^2 = A / (4 pi) - r^2   ("spin" a = J/M = specific angular momentum)
! M = (r^2 + a^2) / (2 r)

! J = a M   (angular momentum)

(this is from the thorn's qlm_analyse.F90)

If the assumption is fine with you, you can just use this estimate.

2) qlm_spin is equation (25) in http://arxiv.org/pdf/gr-qc/0206008.pdf
(in a nutshell, it involves identifying a rotational symmetry on the
surface and constructing the corresponding conserved charge);

3) qlm_npspin and qlm_wsspin are measures of angular momentum based on
the Newman-Penrose coefficients and Weyl scalars, respectively (for an
example of what the integrands look like on e.g. Kerr, you can take a
look at Chapter 6 of Chandrasekhar's book);

4) qlm_cvspin is, as far as I can tell, currently not set;

5) qlm_coordspin* is the same as 2), but assuming that the generators of
the rotational symmetry are the x, y, and z axis, respectively.

> Also: what's the difference between qlm_polar_circumference_0 and
> qlm_polar_circumference_pi_2?

These are the length of the meridians at phi=0 and phi=pi/2, respectively.

Best,
Eloisa
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