Solving the Hamiltonian constraint for 1+log trumpets

Understand

The puncture method specifies black hole data on a hypersurface with the aid of a conformal rescaling of the metric that exhibits a coordinate singularity at the puncture point.

• When constructing puncture initial data by solving the Hamiltonian constraint for the conformal factor, the coordinate singularity requires special attention.
• The standard way to treat the pole singularity occurring in wormhole puncture data is not generally applicable to trumpet puncture data.
• We investigate a new approach based on inverse powers of the conformal factor and present numerical examples for single punctures of the wormhole and 1+log-trumpet type.