2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112381Initial data for boosted Kerr black hole are constructed in an axially symmetric case. Momentum and hamiltonian constraints are solved numerically using finite element method (FEM) algorithms. Both Bowen-York and puncture boundary conditions are adopted and appropriate results are compared. Past and future apparent horizons are also found numerically and the Penrose inequality is tested in detail.18 pages, 6 figuresGeneral Relativity and Quantum Cosmologytext