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[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 259)
by tanja.bode＠physics.gatech.edu 05 Mar '12

05 Mar '12

User: tbode Date: 2012/03/05 04:00 PM Modified: / ET.tex Log: Clear up TOV solver atmosphere statement. File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +2 -2 =================================================================== --- ET.tex 2012-03-05 21:01:13 UTC (rev 258) +++ ET.tex 2012-03-05 21:59:59 UTC (rev 259) @@ -1048,13 +1048,13 @@ $\Phi$ the logarithm of the lapse. The routine also supplies the analytically known solution in the exterior, \begin{eqnarray} - P & = & {\tt TOV\_atmosphere},\nonumber \\ + P & = & P({\tt TOV\_atmosphere}),\nonumber \\ m & = & M, \nonumber\\ \Phi & = &\dfrac{1}{2} \log(1-2M / r) \label{eq:TOVexterior} \end{eqnarray} where {\tt TOV\_atmosphere} is a parameter used to specify the density of the -ambient atmosphere. Since the isotropic radius $\bar{r}$ is the more +ambient atmosphere and a polytropic equation of state is assumed. Since the isotropic radius $\bar{r}$ is the more commonly preferred choice to initiate dynamical calculations, the code then transforms all variables into isotropic coordinates, integrating the radius conversion formula

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[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 258)
by diener＠cct.lsu.edu 05 Mar '12

05 Mar '12

User: diener Date: 2012/03/05 03:01 PM Modified: / ET.tex Log: Make the relationship between M_{bh}, M_{AH} and M_{IH} more clear. File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +10 -3 =================================================================== --- ET.tex 2012-03-05 20:31:26 UTC (rev 257) +++ ET.tex 2012-03-05 21:01:13 UTC (rev 258) @@ -2333,7 +2333,7 @@ \includegraphics[width=0.9\textwidth]{ah_mass_conv} \caption{The top plot shows the irreducible mass of the apparent horizon as a function of time at low (black solid curve), medium (blue dashed curve) -and high (red dotted curve) resolutions. The inset is a zoom in on the +and high (red dotted curve) resolutions. The inset is a zoom in on the $y$-axis to more clearly show the differences between the resolutions. The bottom plot shows the convergence of the irreducible mass. The black (solid) curve shows the difference between the medium and low resolution results, @@ -2342,6 +2342,9 @@ difference between the high and medium resolutions scaled according to fourth and third-order convergence respectively.} \label{fig:ah_mass} \end{figure} +Note that the irreducible mass +$M_{\mathrm{AH}}$ is smaller than the initial mass $M_{\mathrm{bh}}$ due to +the spin of the black hole. The inset shows in more detail the differences between the different resolutions. The irreducible mass increases by about 0.3\% during the first $40\mathrm{M}$ of evolution and then remains constant (within numerical error) for the @@ -2358,8 +2361,12 @@ to the horizon location at the lowest resolution. Finally, in Figure~\ref{fig:ah_mass_spin} we show the total -mass (top plot) and the change in the spin, $\Delta S = S(t) - S(t=0)$, as -calculated by \codename{QuasiLocalMeasures}. +mass $M_{\mathrm{IH}}$ (top plot) and the change in the spin, $\Delta S = S(t) - S(t=0)$, as +calculated by \codename{QuasiLocalMeasures}. The total mass $M_{\mathrm{IH}}$ +is calculated using the Christodoulou formula (see +equation~(\ref{eq:christodoulou})) and initially agrees with +$M_{\mathrm{bh}}$ but then starts to increase due to the flux of gravitational +wave energy through the horizon. \begin{figure} \includegraphics[width=0.9\textwidth]{qlm_mass} \includegraphics[width=0.9\textwidth]{qlm_spin}

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[svn:einsteintoolkit] manifest/trunk/ (Rev. 155)
by bcmsma＠astro.rit.edu 05 Mar '12

05 Mar '12

User: bmundim Date: 2012/03/05 02:39 PM Modified: /trunk/ einsteintoolkit.bib Log: Fix a typo. File Changes: Directory: /trunk/ ================== File [modified]: einsteintoolkit.bib Delta lines: +1 -2 =================================================================== --- trunk/einsteintoolkit.bib 2012-03-05 20:00:58 UTC (rev 154) +++ trunk/einsteintoolkit.bib 2012-03-05 20:39:36 UTC (rev 155) @@ -896,8 +896,7 @@ @article{Christodoulou:1970wf, author = "Christodoulou, D.", - title = "{Reversible and irreversible transforations in black hole - physics}", + title = "{Reversible and Irreversible Transformations in Black-Hole Physics}" journal = "Phys.Rev.Lett.", volume = "25", pages = "1596-1597",

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[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 257)
by diener＠cct.lsu.edu 05 Mar '12

05 Mar '12

User: diener Date: 2012/03/05 02:31 PM Modified: / ET.tex Log: Make the equation defining the irreducible mass a displayed equation so I can refer to it later. File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +8 -4 =================================================================== --- ET.tex 2012-03-05 20:09:52 UTC (rev 256) +++ ET.tex 2012-03-05 20:31:26 UTC (rev 257) @@ -1866,9 +1866,12 @@ There are also the quasi-local measures of mass and angular momentum, from any \ahz{s} found during the spacetime. Both \codename{AHFinderDirect} and \codename{AHFinder} output the -corresponding irreducible mass derived from the area of the horizon -$M_{\mathrm{ir}} = -\sqrt{A/(16\pi)}$. Note that the irreducible mass is smaller than the total +corresponding irreducible mass $M_{\mathrm{ir}}$ derived from the area of the horizon +\begin{equation} +M_{\mathrm{ir}} = +\sqrt{\frac{A}{16\pi}}. \label{eq:irreducible} +\end{equation} +Note that $M_{\mathrm{ir}}$ is smaller than the total mass if the black hole is spinning. The module \codename{QuasiLocalMeasures} implements @@ -2321,7 +2324,8 @@ Since there is non-trivial gravitational wave content in the initial data, the mass of the BH changes during its evolution. In figure~\ref{fig:ah_mass}, -we show in the top plot the irreducible mass as calculated by +we show in the top plot the irreducible mass (see +equation~(\ref{eq:irreducible})) as calculated by \codename{AHFinderDirect} as a function of time at the high (black solid curve), medium (blue dashed curve) and low (red dotted curve) resolutions. \begin{figure}

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[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 256)
by diener＠cct.lsu.edu 05 Mar '12

05 Mar '12

User: diener Date: 2012/03/05 02:09 PM Modified: / ET.tex Log: Add equal-mass to the main text where figure 7 is described. File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +1 -1 =================================================================== --- ET.tex 2012-03-05 20:01:40 UTC (rev 255) +++ ET.tex 2012-03-05 20:09:52 UTC (rev 256) @@ -2173,7 +2173,7 @@ well suited to current binary BH simulations in which the high-resolution regions are centered on the individual BHs. Figure~\ref{fig:bbh-boxes} shows a typical set of nested boxes during -the inspiral phase of a binary BH merger simulation. +the inspiral phase of an equal-mass binary BH merger simulation. \begin{figure}[htbp] \begin{center} \includegraphics{bbh-boxes}

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[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 255)
by diener＠cct.lsu.edu 05 Mar '12

05 Mar '12

User: diener Date: 2012/03/05 02:01 PM Modified: / ET.tex Log: Added the Christodoulou formula (with reference) and slightly changed the notation. File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +13 -2 =================================================================== --- ET.tex 2012-03-05 18:40:12 UTC (rev 254) +++ ET.tex 2012-03-05 20:01:40 UTC (rev 255) @@ -1866,8 +1866,10 @@ There are also the quasi-local measures of mass and angular momentum, from any \ahz{s} found during the spacetime. Both \codename{AHFinderDirect} and \codename{AHFinder} output the -corresponding irreducible mass derived from the area of the horizon $m_H = -\sqrt{A/(16\pi)}$. +corresponding irreducible mass derived from the area of the horizon +$M_{\mathrm{ir}} = +\sqrt{A/(16\pi)}$. Note that the irreducible mass is smaller than the total +mass if the black hole is spinning. The module \codename{QuasiLocalMeasures} implements the calculation of mass and spin multipoles from the isolated @@ -1885,6 +1887,15 @@ can calculate useful quantities such as the Weyl or Ricci scalars or the three-volume element of the horizon world tube in addition to physical observables such as mass and momenta. +For the calculation of the total mass \codename{QuasiLocalMeasures} uses the +Christodoulou mass~\cite{Christodoulou:1970wf} +\begin{equation} + M^2 = M_{\mathrm{ir}}^2+\frac{S^2}{4 M_{\mathrm{ir}}^2}, +\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 $M$. Finally, the module \codename{HydroAnalysis} additionally locates the (coordinate) center of mass as well as the point of maximum rest mass density of a

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[svn:einsteintoolkit] manifest/trunk/ (Rev. 154)
by diener＠cct.lsu.edu 05 Mar '12

05 Mar '12

User: diener Date: 2012/03/05 02:00 PM Modified: /trunk/ einsteintoolkit.bib Log: Added Christodoulou:1970wf. File Changes: Directory: /trunk/ ================== File [modified]: einsteintoolkit.bib Delta lines: +12 -0 =================================================================== --- trunk/einsteintoolkit.bib 2012-03-05 18:39:20 UTC (rev 153) +++ trunk/einsteintoolkit.bib 2012-03-05 20:00:58 UTC (rev 154) @@ -894,6 +894,18 @@ eprint = "arXiv:1006.2839 [gr-qc]", } +@article{Christodoulou:1970wf, + author = "Christodoulou, D.", + title = "{Reversible and irreversible transforations in black hole + physics}", + journal = "Phys.Rev.Lett.", + volume = "25", + pages = "1596-1597", + doi = "10.1103/PhysRevLett.25.1596", + year = "1970", + SLACcitation = "%%CITATION = PRLTA,25,1596;%%", +} + @article{Colella:1982ee, author = "Colella, Phillip and Woodward, Paul R.", title = "{The Piecewise Parabolic Method (PPM) for Gas

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[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 254)
by diener＠cct.lsu.edu 05 Mar '12

05 Mar '12

User: diener Date: 2012/03/05 12:40 PM Modified: / ET.tex Log: Cite Brandt:1996si when discussing Bowen-York initial data for a distorted spinning black hole. File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +2 -2 =================================================================== --- ET.tex 2012-03-01 05:39:01 UTC (rev 253) +++ ET.tex 2012-03-05 18:40:12 UTC (rev 254) @@ -28,7 +28,7 @@ \usepackage[all]{hypcap} \usepackage[sort&compress,numbers]{natbib} -\renewcommand{\bibfont}{\footnotesize} +%\renewcommand{\bibfont}{\footnotesize} \graphicspath{{figures/} {cactus-benchmarks/} @@ -2241,7 +2241,7 @@ resolution on the finest (coarsest) grid. The runs were performed using the tapering evolution scheme in \codename{Carpet} to avoid interpolation in time during prolongation. The initial data correspond to a rotating, stationary Kerr BH -perturbed by a Brill wave and, as such, has a non-zero +perturbed by a Brill wave\cite{Brandt:1996si} and, as such, has a non-zero gravitational wave content. We evolved the BH using 4th-order finite differencing from $T=0\mathrm{M}$ until it had settled down to a stationary state at $T=120\mathrm{M}$.

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[svn:einsteintoolkit] manifest/trunk/ (Rev. 153)
by diener＠cct.lsu.edu 05 Mar '12

05 Mar '12

User: diener Date: 2012/03/05 12:39 PM Modified: /trunk/ einsteintoolkit.bib Log: Add Brandt:1996si. File Changes: Directory: /trunk/ ================== File [modified]: einsteintoolkit.bib Delta lines: +13 -0 =================================================================== --- trunk/einsteintoolkit.bib 2012-02-17 17:41:13 UTC (rev 152) +++ trunk/einsteintoolkit.bib 2012-03-05 18:39:20 UTC (rev 153) @@ -632,6 +632,19 @@ doi = "10.1103/PhysRevD.76.124038", } +@article{Brandt:1996si, + author = "Brandt, Steven R. and Seidel, Edward", + title = "{The Evolution of distorted rotating black holes. 3: + Initial data}", + journal = "Phys.Rev.", + volume = "D54", + pages = "1403-1416", + doi = "10.1103/PhysRevD.54.1403", + year = "1996", + eprint = "arXiv:gr-qc/9601010", + SLACcitation = "%%CITATION = GR-QC/9601010;%%", +} + @Article{Brandt:1997tf, author = "Brandt, Steven and Br{\"u}gmann, Bernd", title = "{Black hole punctures as initial data for general

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[svn:einsteintoolkit] Workshop_Spring_2012/ (Rev. 2)
by knarf＠cct.lsu.edu 05 Mar '12

05 Mar '12

User: knarf Date: 2012/03/05 11:00 AM Added: / introduction.tex, preamble.tex /pics/ einstein_flip.png Modified: / Log: template Directory Changes: Directory: / ============ Property changes on: ___________________________________________________________________ Directory: /svn:ignore/ ======================= + *.log *.nav *.toc *.out *.aux *.snm Directory: /svn:mime-type/ ========================== + application/octet-stream File Changes: Directory: / ============ File [added]: introduction.tex Delta lines: +26 -0 =================================================================== --- introduction.tex (rev 0) +++ introduction.tex 2012-03-05 17:00:06 UTC (rev 2) @@ -0,0 +1,26 @@ +\input{preamble} +\usepackage{ragged2e} +\usecolortheme[RGB={200,200,200}]{structure} + +\begin{document} + +\begin{frame} \frametitle{What will you learn here?} + \begin{centering} + \textbf{...}\\ + \includegraphics[height=2cm]{einstein_flip.png} + \end{centering} +\end{frame} + +\begin{frame} \frametitle{What do we assume?} + We assume you + \begin{itemize} + \item are able to write, or at least read, a serial code in C/C++/Fortran; + \item ... + \end{itemize} + It would be advantagous (but not necessary) if you + \begin{itemize} + \item are familiar with the Linux/Unix environment + \end{itemize} +\end{frame} + +\end{document} File [added]: preamble.tex Delta lines: +64 -0 =================================================================== --- preamble.tex (rev 0) +++ preamble.tex 2012-03-05 17:00:06 UTC (rev 2) @@ -0,0 +1,64 @@ +\documentclass{beamer} + +\usepackage[utf8]{inputenc} +\usepackage{beamerthemesplit} +\usepackage{url} +\usepackage{hyperref} +\usepackage{tikz} +\usepackage{alltt} + +\usetheme{Madrid} +\definecolor{cactusgreen}{RGB}{132,186,75} +\graphicspath{{pics/}} + +\newcommand{\ilshell}[1]{\colorbox{lightgray}{\small{\texttt{#1}}}} +\newcommand{\shell}[1]{\hspace{1cm}\colorbox{lightgray}{\small{\texttt{#1}}}} + +\hyphenation{Cac-tus-Ein-stein Schwarz-schild vacuum in-fra-struc-ture} + +% \logo{\includegraphics[height=1cm]{pics/cactuslogo.png}} + +% We want to use the infolines outer theme because it uses so less space, but +% it also tries to print an institution (which we do not have) and the slide +% numbers (which we might not want to show). Therefore, we here redefine the +% footline ourselfes - mostly a copy & paste from +% /usr/share/texmf/tex/latex/beamer/themes/outer/beamerouterthemeinfolines.sty +\defbeamertemplate*{footline}{infolines theme without institution and slide numbers} +{ + \leavevmode% + \hbox{% + \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{author in head/foot}% + \usebeamerfont{author in head/foot}\insertshortauthor + \end{beamercolorbox}% + \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{title in head/foot}% + \usebeamerfont{title in head/foot}\insertshorttitle + \end{beamercolorbox}% + \begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{date in head/foot}% + \usebeamerfont{date in head/foot}\insertshortdate{} + \end{beamercolorbox}}% + \vskip0pt% +} + +% For some reason this is not displayed by default. This is just a copy & paste +% from the same file as the footline +\defbeamertemplate*{headline}{infolines theme with sections/subsections} +{ + \leavevmode% + \hbox{% + \begin{beamercolorbox}[wd=.5\paperwidth,ht=2.25ex,dp=1ex,right]{section in head/foot}% + \usebeamerfont{section in head/foot}\insertsectionhead\hspace*{2ex} + \end{beamercolorbox}% + \begin{beamercolorbox}[wd=.5\paperwidth,ht=2.25ex,dp=1ex,left]{subsection in head/foot}% + \usebeamerfont{subsection in head/foot}\hspace*{2ex}\insertsubsectionhead + \end{beamercolorbox}}% + \vskip0pt% +} + +\newcommand{\abspic}[4] + {\vspace{ #2\paperheight}\hspace{ #3\paperwidth}\includegraphics[height=#4\paperheight]{#1}\\ + \vspace{-#2\paperheight}\vspace{-#4\paperheight}\vspace{-0.0038\paperheight}} + +% Make a todo comment stand out visually +\newcommand{\todo}[1]{{~\textbf{\color{red}[TODO: #1]}}} + + Directory: /pics/ ================= File [added]: einstein_flip.png Delta lines: +0 -0 =================================================================== (Binary files differ) Property changes on: pics/einstein_flip.png ___________________________________________________________________

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