Bernard Kelly deleted The_BowenYork_soluti.tex  about 10 years ago

Commit id: a7e772fe9ad432fabb09b46e4b415d42d922cdf1

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The Bowen-York solution (\ref{eq:by_general}) with only linear  momentum is given by taking only the ``$P$'' term of  (\ref{eq:by_K_P_S}). This is parametrised by the ADM linear momentum  $P$:  & & \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]  where the conformal factor $\psi$ must satisfy the Hamiltonian  constraint. Gleiser et al \cite{Gleiser:1999hw} have produced a  slow-moving approximate solution for the conformal factor $\psi$, with  two types of inner boundary conditions: inversion symmetric throat  conditions, and puncture conditions. I quote here only the result of  the latter choice, assuming the hole has momentum $P$ in the  positive-$z$ direction:         

In_practice_the_boos.tex  subsectionLinearly_M.tex  brace_psi__psi0R.tex  The_BowenYork_soluti.tex