Hello Gwyneth and Eloisa, On Thu, Mar 2, 2017 at 8:31 AM, Eloisa Bentivegna < [email protected]> 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 > _______________________________________________ > Users mailing list > [email protected] > http://lists.einsteintoolkit.org/mailman/listinfo/users >
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