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When using the black hole exclusion (horizon boundary condition) technique,$K$ is usually nonzero and spatially variable, so none of the special cases ofYork's conformal-decomposition algorithm apply, and the full 4-vector nonlinearYork equations must be solved numerically.  We discuss the construction of dynamic black hole initial data slices usingthis technique: We perturb a known black hole slice via some Ansatz, apply theYork decomposition (using another Ansatz for the inner boundary conditions) toproject the perturbed field variables back into the constraint hypersurface,and finally optionally apply a numerical 3-coordinate transformation to (eg)restore an areal radial coordinate.  In comparison to other initial data algorithms, the key advantage of thisalgorithm is its flexibility: $K$ is unrestricted, allowing the use of whateverslicing is most suitable for (say) a time evolution.  We have implemented this algorithm for the spherically symmetric scalar fieldsystem. We present numerical results for a number of Eddington-Finkelstein--like initial data slices containing black holes surrounded byscalar field shells. Using 4th order finite differencing with resolutions of$\Delta r/r \approx 0.02$ (0.01) near the (Gaussian) perturbations, thenumerically computed energy and momentum constraints for the final slices are$\ltsim 10^{-8}$ ($10^{-9}$) and $\ltsim 10^{-9}$ ($10^{-10}$) in magnitude.  Finally, we briefly discuss the errors incurred when interpolating data fromone grid to another, as in numerical coordinate transformation or horizonfinding. We show that for the usual moving-local-interpolation schemes, evenfor smooth functions the interpolation error is not smooth.Comment: [revised to correct error in integrated-scalar-field mass function  defn, changed title and author address, assorted lesser changes] REVTeX, 45  pages, 25 figures + 1 rotated table, uses rotate.sty and natbib.sty  (included), to appear in PRD1

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

A<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>computational scheme for dynamic spherically symmetric black hole spacetimes: Initial data

A3+1computational scheme for dynamic spherically symmetric black hole spacetimes: Initial data