Multiple-throat Misner data

The generalisation of the above form of data to multiple black holes is available as the multiple_misner_bh initial data set. The conformal factor is determined by recursively applying a Misner isometry condition to each of the black holes relative to the others.

The black holes are arranged at equal-spaced angles on a circle around the origin in the $xy$-plane. The radius of the circle is $\coth\mu_0$, where $\mu _0$ is given by the idanalyticbh::mu parameter, and the first black hole lies on the $x$-axis (as in Figure D12.6).

Figure D12.2: Configuration for three Misner throats using the multiple_misner_bh initial data.

[height=40mm]/home/cactus_web/CheckOut/CactusStable/arrangements/CactusEinstein/IDAnalyticBH/doc/multi_misner

The number of throats is given by the parameter idanalyticbh::misner_nbh, which defaults to 1 and has a hard-coded upper limit of 10. The number of terms used in the Misner expansion is controlled by the parameter idanalyticbh::nmax, which has a default value of 30.

For this version of the Misner data, derivatives of the conformal factor $\psi$ are determined numerically by finite differencing, using values of $\psi$ calculated at small distances from the point at which the derivative is to be evaluated. The size of the numerical stencil is hardcoded at $dx=10^-6$.

As an example, a parameter file implementing 3 Misner black holes on a circle of radius $\cosh 4$ would use the following parameters:

  ActiveThorns = "... ADMBase StaticConformal IDAnalyticBH ..."

  admbase::metric_type = "static conformal"

  admbase::initial_data = "multiple_misner_bh"

  idanalyticbh::misner_nbh = 3
  idanalyticbh::mu = 4