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Using a constrained formalism for Einstein equations in Dirac gauge, wepropose to compute excised quasistationary initial data for black holespacetimes in full general relativity. Vacuum spacetime settings arenumerically constructed by using the isolated horizon formalism; we especiallytackle the conformal metric part of our equations, assuming globalstationarity. We show that a no-boundary treatment can be used on the horizonfor the equation related to the conformal metric. We relate this finding toprevious suggestions in the literature, and use our results to assess thewidely used conformally flat approximation for computing black hole initialdata.

Isolated horizons in numerical relativity: constructing the excised Kerr spacetime in Dirac gauge