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In this talk I will briefly present the Fully Constrained Formulation as framework used to construct initial data for Einstein equations consistent with Hamiltonian and momentum constraints. I will use it to construct constraint satisfying initial data for isolated rotating neutron star, Gaussian and toroidal configurations of self-gravitating scalar fields, and binary systems of compact objects. I will compare the last cases with other commonly-used strategies that do not actually solve the constraint equations initially.
Andrew Lundgren, Lluïsa-Maria Mir