Abstract
1 Introduction
1.1 Conventions
2 The Initial-Value Equations
2.1 Initial Data
2.2 York-Lichnerowicz Conformal Decompositions
2.3 Conformal Thin-Sandwich Decomposition
2.4 Stationary Solutions
3 Black Hole Initial Data
3.1 Classic Solutions
3.2 General Multi-Hole Solutions
3.3 Horizon-Penetrating Solutions
3.4 Quasicircular Binary Data
4 Neutron-Star Initial Data
4.1 Hydrostatic Equilibrium
4.2 Isolated Neutron Stars
4.3 Neutron-Star Binaries
5 Acknowledgments
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