deletions | additions       diff --git a/Bowen__York_citeBowe.tex b/Bowen__York_citeBowe.tex  index 3a3bd44..96f60a8 100644  --- a/Bowen__York_citeBowe.tex  +++ b/Bowen__York_citeBowe.tex 
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Bowen \& York \cite{Bowen:1980yu} \citet{Bowen:1980yu}  introduced a set of partial solutions to the constraint equations, where the momentum constraint is solved automatically by extrinsic curvature that can incorporate bulk ADM linear and/or angular momentum. The data is not completely determined -- there is a conformal factor $\psi$ that must be found by solving the Hamiltonian constraint elliptic equation. The physical metric quantities are: %   \begin{equation}   \label{eq:by_general}   \gamma_{i j} = \psi^4 \delta_{i j} \;\; , \;\; K_{i j} = \psi^{-2} \hat{K}_{i j},   \end{equation}   %  where the conformal extrinsic curvature contains angular- and/or and/  linear-momentum terms: & %   %   \begin{array}   \label{eq:by_K_P_S}   \hat{K}_{i j} &= frac{3}{r^3}\left[ \epsilon_{k i m} \, S^m \, n^k \, n_j + \epsilon_{k j m} \, S^m \, n^k \, n_i \right] \nonumber \\  & + \frac{3}{2 r^2}\left[ P_i \, n_j + P_j \, n_i - (\delta_{i j} - n_i \, n_j ) P^k \, n_k \right] \\ &&  \mp \frac{3 a^2}{2 r^4}\left[ P_i \, n_j + P_j \, n_i + (\delta_{i j} - 5 n_i \, n_j) P^k \, n_k \right] \nonumber, \end{array}   %  where $r$ is a conformal radial coordinate, centred on the singularity. The factor $\psi$ then must be found by solving the Poisson-like vacuum Hamiltonian constraint: %   \begin{equation}   \label{eq:by_ham_const}   \Delta \psi + \frac{1}{8} \psi^{-7} \hat{K}_{i j}\hat{K}^{i j} = 0.   \end{equation}