User: knarf Date: 2012/03/13 09:49 AM
Modified: / ET.tex
Log: fix newly introduced typos
File Changes:
Directory: / ============
File [modified]: ET.tex Delta lines: +6 -6 =================================================================== --- ET.tex 2012-03-13 14:41:53 UTC (rev 306) +++ ET.tex 2012-03-13 14:49:04 UTC (rev 307) @@ -1195,7 +1195,7 @@ \end{figure}
\codename{Meudon_Bin_BH} can read in BH-BH binary initial data described -in~\cite{Grandclement:2001ed}, representing solutions to the hamiltonian and momentum constraints, along with the trace of the spatial components of the Einstein equations, form the linked elliptic equation set: +in~\cite{Grandclement:2001ed}, representing solutions to the Hamiltonian and momentum constraints, along with the trace of the spatial components of the Einstein equations, form the linked elliptic equation set: \begin{eqnarray*} &&\nabla^2\alpha_{(m)} = \alpha \psi^4 K_{ij} K^{ij}_{(m)}\ &&\nabla^2\psi_{(m)}=-\frac{\psi^5}{8}K_{ij}K^{ij}_{(m)}\ @@ -2081,8 +2081,8 @@ \label{eq:christodoulou} \end{equation} that takes into account the -contributions of the irreducuble mass $M_{\mathrm{ir}}$ and angular -momemtum $S$ to the total black hole mass $M$. +contributions of the irreducible mass $M_{\mathrm{ir}}$ and angular +momentum $S$ to the total black hole mass $M$.
Finally, the module \codename{HydroAnalysis} additionally locates the (coordinate) center of mass as well as the point of maximum rest mass density of a @@ -2496,7 +2496,7 @@ extracted at $R=30\mathrm{M}$, and its numerical convergence. In this and in the following sections, a numerical quantity $\Psi$ is said to converge with convergence order $Q$ if for a set of numerical -stepsizes $h_1$, $h_2$, $h_3$ the difference between successive +step sizes $h_1$, $h_2$, $h_3$ the difference between successive resolutions scales as \begin{equation} \frac{\Psi_{h_1}-\Psi_{h_2}}{\Psi_{h_2}-\Psi_{h_3}} = \frac{h_1^Q-h_2^Q}{h_2^Q-h_3^Q},. @@ -3021,8 +3021,8 @@ star's coordinate radius is twice the size of the forming apparent horizon~\cite{Thierfelder:2010dv}. At this point the majority of the matter is inside the apparent horizon, whose size quickly grows to its -final size while the numerical spacetime aproaches the final ``trumpet'' -configuraton. +final size while the numerical spacetime approaches the final ``trumpet'' +configuration.
In Figure~\ref{fig:tov_collapse_H_convergence_at0}, we display the convergence factor for the Hamiltonian constraint