User: eschnett Date: 2011/11/14 01:05 PM
Modified: / ET.tex
Log: Small whitespace corrections
File Changes:
Directory: / ============
File [modified]: ET.tex Delta lines: +2 -2 =================================================================== --- ET.tex 2011-11-14 18:11:02 UTC (rev 238) +++ ET.tex 2011-11-14 19:05:49 UTC (rev 239) @@ -225,7 +225,7 @@ without requiring exorbitant computational resources, though some BH-NS simulations have been performed with a pseudospectral code \cite{Duez:2008rb,Duez:2009yy,Foucart:2010eq,Foucart:2011mz}. Many groups' codes now include GRMHD (used widely for NS-NS mergers, and for BH-NS mergers in~\cite{Chawla:2010sw}, and some include microphysical effects as -well~(e.g.,\cite{Duez:2009yy,Sekiguchi:2011zd,Sekiguchi:2011mc}). +well~(e.g.,~\cite{Duez:2009yy,Sekiguchi:2011zd,Sekiguchi:2011mc}).
In addition to studying binary mergers, numerical relativity is a necessary element for understanding stellar collapse and dynamical instabilities @@ -916,7 +916,7 @@ \end{eqnarray} where the sub/superscript $(m)$ refers to the contribution from BH $m=1,2$; the 3-momentum is $p^i$; the BH spin angular momentum is $S_i$; the conformal 3-metric -$\gamma^{ij}$ is assumed to be flat, i.e. $\gamma_{ij}=\eta_{ij}$, and $\hat{N}^i=x^i/r$ +$\gamma^{ij}$ is assumed to be flat, i.e.\ $\gamma_{ij}=\eta_{ij}$, and $\hat{N}^i=x^i/r$ is the Cartesian normal vector relative to the position of each BH in turn. This solution automatically satisfies the momentum constraint, and the Hamiltonian constraint may be written as an elliptic equation for the conformal factor, defined by the condition $g_{ij}=\psi^4\gamma_{ij}$ or equivalently $\psi\equiv (\det|g_{ij}|)^{1/12}$: