Initial Condition Solver

Initial Condition Solver

This tool is currently located in Experimental Tools.

What is it?

Any arbitrarily chosen data for the metric and sources will not necessarily be physical. The purpose of the initial condition solver is to generate data which is consistent with the Hamiltonian and Momentum constraints of GR.

What does it do?

Currently the initial condition solver solves only the Hamiltonian constraint of GR under a number of specific conditions - primarily the data must be a superposition of 2 black holes and a scalar field.

It outputs data in a format which can be read in as a starting checkpoint file for the main GRChombo time evolution.

The AMR regrid condition is set by the magnitude of the source terms plus the conformal factor psi (to enforce regridding around punctures).

The run time is of order 5-10 minutes on 24 cores.

The conditions and assumptions are listed below.

Bowen York data for 2 black holes

One may specify in the params.txt files the masses, momenta and spins for 2 black holes. The solver will solve for the correction dpsi to the conformal factor psi as a result of the non zero spin and momenta.

A general scalar field configuration

One may specify the values of the scalar field phi by position in the file MyPhiFunction.H. The solver will solve for the correction dpsi to the conformal factor psi as a result of the non zero source.

Periodic or asymptotically flat boundary conditions

The solver can solver under the assumption of periodic boundary conditions (even in the presence of black holes), or asymptotically flat data.

If periodic boundary conditions are specified, the value of the trace of the extrinsic curvature K is set to a constant across the grid to ensure that the integrability condition is satisfied (ie, so that the conformal factor psi is periodic).

General assumptions:

1. The Momentum constraint is satisfied by the chosen data for \bar A_ij. (If Bowen York data is used this will automatically be the case.)

2. K is a constant across the grid, either set to zero for asymptotically flat data, or a constant set by the integrability condition for periodic boundaries.

3. The metric is conformally flat (\tilde \gamma_ij = \delta_ij).

4. The time derivative of the scalar field Pi = dphidt = 0.

5. The lapse is set to 1 and the shift components to zero.

What are the key files?

The params.txt file contains the parameters for the run, which may be amended by the user.

The solver process is best seen by reading the Main_PoissonSolver.cpp file.

One should also look at the SetLevelData.cpp file to see how the position dependent coefficients of the solver are set.