Thanks Eloisa,
2015. 6. 26. 오후 8:50에 "Eloisa Bentivegna" eloisa.bentivegna@ct.infn.it님이 작성:
On 25/06/15 05:07, Hee Il Kim wrote:
Hi, Recently, I found the multipole moment calculations in QuasiLocalMeasures show large errors, e.g. 20% for the second mass moment of my project.[...]
I understand. But the issue is, even though I'm using sufficiently high resolution for my collapsing star study, the code calculates inaccurately the higher multipole moments for n >0, where n is the order of the Legendre polynomial. So it calculates the mass and the spin very accurately.
Dear Hee Il,
thanks for reporting the issue. May I ask: how are you testing the code? Which quantities are you comparing to the output of QLM, and how did you obtain them (a formula, another code, etc.)?
What I have checked is actually to see whether the QLM results satisfy the no-hair theorem of Kerr black holes, i.e., to see whether,
M_0 = M_bh, M_2 = -(J_bh)^2/M_bh, ...
J_1= J_bh, J_3 = -(J_bh)^3/(M_bh)^2, ... , when the bh formed in the simulation becomes stationary.
E.g.,
plot "quasilocalmeasures::qlm_multipole_moments..asc" u 9:(-$23*$23/$13) replot "quasilocalmeasures::qlm_multipole_moments..asc" u 9:15
where $23=M_bh, $13=J_bh, and the 15th column of the data represents the 2nd mass multipole moment of the bh.
I see that you mention a collapsing star: what multipoles are you calculating in that case? QLM only computes the geometric multipoles of 2D surfaces (and not, for instance, of the matter density). Does an apparent horizon form in your simulation, and in that case, is this what you are calculating the multipoles of?
Sorry for the confusion. The multipole, here, means the mutipole moment of the black hole found by the horizon finder (AHFinderDirect), not the multipole moment of matter.
Cheers,
Hee Il