= Numerical relativity
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<Numerical relativity> computes solutions of the <Einstein field equations> when an analytic solution or a small-perturbation approximation is insufficient. A <3+1 decomposition of spacetime> separates initial spatial geometry and matter from their subsequent evolution. Initial data must satisfy the <Hamiltonian constraint> and <momentum constraint>, while the <lapse function> and <shift vector> specify the coordinate evolution.
The calculation also needs boundary conditions and a numerical evolution formulation. Resolution studies, constraint monitoring and comparison with known solutions test whether the computed result approximates the intended spacetime. Binary black-hole mergers provide an observational application: numerical waveforms connect strongly dynamical geometry with interferometer signals.<Observation of Gravitational Waves from a Binary Black Hole Merger by B. P. Abbott and others>[Waveform comparison with the predicted inspiral, merger and ringdown]{ref} Extracting a physical wave requires controlling the frame and propagation model as well as solving grid equations.
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