2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/196845We solve the elliptic equations associated with the Hamiltonian and momentum constraints, corresponding to a system composed of two black holes with arbitrary linear and angular momentum. These new solutions are based on a Kerr-Schild spacetime slicing which provides more physically realistic solutions than the initial data based on conformally flat metric/maximal slicing methods. The singularity/inner boundary problems are circumvented by a new technique that allows the use of an elliptic solver on a Cartesian grid where no points are excised, simplifying enormously the numerical problem.4 pages, 3 figures. Minor corrections, some points clarified, and one reference added. To appear in Phys. Rev. LettGeneral Relativity and Quantum CosmologyAstrophysicstext