Black hole initial data (Harald Pfeiffer  -- Cook & Pfeiffer, 2004) 

All initial-data sets were prepared with the same pipe-line: The
extented conformal thin sandwich equations are solved to obtain (psi,
beta^i, N*psi) up to the apparent horizon.  The coordinate radius of
the apparent horizon differs with changing slicings, boundary
conditions, etc.  It is chosen such that the black holes have unit
mass in the limit of large separation.  The outer boundary of the
data-set is generally around 1e10 to 1e15.  After the ellitpic
equations are solved, (psi, beta^i, N*psi) are extrapolated radially
inward by 12-th order polynomial extrapolation to a new inner radius
25 per cent smaller than r_{AH}.  Finally, spatial metric, extrinsic
curvature, lapse and shift are assembled and written to disk.

Note that the extrapolation does NOT take the constraints into
account.  While the constraints will be very well satisfied outside
r_{AH}, constraint violations become larger as one goes further inside
the horizon.
 

Each archive contains the following files: 

- Subdirectories LevX (where 'X' is a digit), containing the data at
  different resolutions. 'X' denotes the refinement factor; large 'X'
  being high resolution.  Interpolations of higher resolution data
  sets takes longer, thus, the low-resolution data sets may come in
  handy to speed up interpolation while debugging interpolation
  routines.

  
- A text file "Convergence," containing some information about the
  convergence of each resolution.  The rows corresponds to different
  resolutions, starting with Lev0 (so that "Lev3" corresponds to
  the fourth row).  The colums mean
    1. N        - cube-root of number of collocation points 
    2. Nor-Linf - maximal difference of (psi, beta, Npsi) at the
                  collocation points between this resolution and 
                  the next-LOWER one.
    3. Nor-L2   - as Nor-Linf, but root-mean-square difference
    4. Ham-Linf - maximal residual of the Hamiltonian constraint 
                  at the collocation points 
    5. Ham-L2   - ditto, but root-mean-square difference 
    6. Mom-Linf - maximal residual of the momentum constraint 
                  at the collocation points 
    7. Mom-L2   - ditto, but root-mean-square difference

  These quantities are obtained from the original elliptic solution,
  i.e. they do NOT take into account constraint violations occuring in
  the extrapolated regions. 


- A text file "Omega," containing the unscaled orbital angular
  frequency for this data set (if appliable).  This number needs to be
  passed into the function ReadData (see PublicID.hpp).  

  Note: Omega is adjusted so that Komar-mass and ADM-energy are equal.
  However, this adjustment has been performed on the comparatively
  coarse resolution Lev2.  Therefore, ADM-energy and Komar-mass coincide
  only to the truncation error of Lev2.

- A text file "AdmQuantities," containing a couple of
  characteristic numbers of the inital data set for each resolution. 
  Some more important ones: 
    N           - cube-root of the number of collocation points
    J_ADM[2]    - unscaled ADM angular momentum (z-component)
    Sph-Exp_MAH - irreducible mass (i.e. sqrt(Area/16 pi) )  
                     of each apparent horizon
    EADM_corr (the first one)   - ADM-energy 
    EADM_corr (the second one)  - ADM-energy minus twice the Komar-mass 
                  
    Each row in "AdmQuantites" corresponds to one particular resolution,
    starting with Lev0.  Initial data supplied in a subdirectory "Lev3"
    corresponds to the fourth row.