Black hole initial data by numerical integration of the parabolic-hyperbolic form of the constraints

Understand

The parabolic-hyperbolic form of the constraints is integrated numerically.

• The applied numerical stencil is $4^{th}$ order accurate (in the spatial directions) while 'time'-integration is made by using the method of lines with a $4^{th}$ order accurate Runge-Kutta scheme.
• The proper implementation of the applied numerical method is verified by convergence tests and monitoring the relative and absolute errors determined by comparing numerical and analytically known solutions of the constraints involving boosted and spinning vacuum single black hole configurations.
• The main part of our investigations is, however, centered on construction of initial data for distorted black holes which, in certain cases, have non-negligible gravitational wave content.