Early graxi merger result (Jan. 26 2001).

The following animations show a `marginal' merger event, with the following characteristics ( id_bh  -- note: uses new parameters not available in current distribution!) :

Rho max: 40
Z min/max: -+40
grid resolution: 128x256
initial coordinate separation of peaks of scalar field: 20
initial proper distance between peaks: 97
initial proper distance between excised regions: 84
proper distance between excised regions just prior to merging: 53
initial single BH mass estimates: 10.1 each
initial merged mass estimate: 17.3
final mass estimate(t=542, run time on maci ~ 40 hours): 13.2
(mass estimates based upon area of outermost trapped surface detected).

psi X 5, colour scale [0.85,2.0]:   psi_5.mpg   (1 MB)
beta_z X 75, variable colour scale:  beta_z_75.mpg  (1 MB)
phi X 100, variable colour scale (hence the occasional 'jitter') :   phi_100.mpg  (1.9 MB)

(the frames are distributed uniformly in time till t=542)

Feb. 8 2001 Updates:

The first example above used free evolution for Psi. However, after excision we can switch to fully constrained evolution without worrying about MG crashing. The benefit of this is that the 1/r boundary condition for Psi works alot better with constrained evolution, especially when the outer boundary is close. In particular we get better mass conservation, and no 'dip' develops in Psi at zmin/max at late times. So here is Psi for the same initial data as above, but switching to constrained evolution at t=15: psi_ri_10.mpg  (2.9 MB --- a longer run, and I changed the scales a bit (sorry)).

The following animations show a merger of black holes created from boosted scalar field collapse (boosted towards each other with v=0.05), where the pulses are initially at a coordinate separation of 40 (twice as far as above). In this case we actually loose track of the trapped region before the merger, but extrapolate the motion to 'force' a merger --- see the outward null expansion animation. id file: id_bh 

alpha:   alpha_768x576.mpg   (4.5 MB)
phi*r (with adjusting scale):  boost_phir.mpg  (7.9 MB)
outgoing null expansion (I can't changed the colormap with the data-vault yet, so excuse the rather horrible color contrast between positive/negative expansion) :   boost_exp.mpg  (2.9 MB)

I recently added a grid function to output Psi4, one of the Newmann-Penrose scalars (with the null tetrad constructed to measure outgoing radiation in the r-direction). The following is from a run for the same boosted initial data as above, but with outer boundary twice as far away: boostf_psi4.mpg  (1.3 MB) The run actually went till t=340 in the 60 hours I asked for on Maci, but there was a bug in the merger code that didn't stopped the extrapolated merger at z=0, so the 'holes' moved through and away from each other, and the excised region just kept growing after t=200. This problem didn't crop up in the earlier example where the outer boundary was closer in, as for some reason in that case a single trapped region was found soon enough. I'm re-running the job with the bug (hopefully) fixed.

As another example of Psi4, I ran a simulation of an initially spherical black hole, perturbed by a brill wave --- id file: id_bh :

sigmabar : sph_brill_sig.mpg  (1.5 MB)

[Psi4*r]^2, variable scales: sph_brill_psi4r2.mpg  (2.5 MB)

d/dt([Psi4*r]^2), and with a fixed color-scale, to highlight behaviour near the hole: sph_brill_ddt_psi4r2.mpg  (6.7 MB) (this animation doesn't decode properly on my pc at home --- if it gives problems for you too, let me know and I'll remake it).