Thanks for the help Eloisa and Vassili! I really appreciate it. Gwyneth
On Thu, Mar 2, 2017 at 6:51 PM, Vassilios Mewes <[email protected]> wrote: > 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 >> > > Disclaimer - University of Cape Town This e-mail is subject to UCT > policies and e-mail disclaimer published on our website at > http://www.uct.ac.za/about/policies/emaildisclaimer/ or obtainable from +27 > 21 650 9111 <+27%2021%20650%209111>. If this e-mail is not related to the > business of UCT, it is sent by the sender in an individual capacity. Please > report security incidents or abuse via [email protected] > > _______________________________________________ > Users mailing list > [email protected] > http://lists.einsteintoolkit.org/mailman/listinfo/users > >
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