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We present a single domain Galerkin-Collocation method to calculate punctureinitial data sets for single and binary, either in the trumpet or wormholegeometries. The combination of aspects belonging to the Galerkin and theCollocation methods together with the adoption of spherical coordinates in allcases show to be very effective. We have proposed a unified expression for theconformal factor to describe trumpet and spinning black holes. In particular,for the spinning trumpet black holes, we have exhibited the deformation of thelimit surface due to the spin from a sphere to an oblate spheroid. We have alsorevisited the energy content in the trumpet and wormhole puncture data sets.The algorithm can be extended to describe binary black holes.

Puncture black hole initial data: a single domain Galerkin-Collocation method for trumpet and wormhole data sets