User: tbode Date: 2011/04/12 05:46 AM

Modified: / ET.tex

Log: Conform to SPIRES bibtex keys.

File Changes:

Directory: / ============

File [modified]: ET.tex Delta lines: +6 -6 =================================================================== --- ET.tex 2011-04-11 22:24:34 UTC (rev 54) +++ ET.tex 2011-04-12 10:46:47 UTC (rev 55) @@ -1202,13 +1202,13 @@ where $n^i$ is the unit outgoing normal to the 2-surface.

The module \codename{AHFinder} provides two algorithms for locating -\ahz{s}. The minimization algorithm~\cite{Anninos98b} finds the local +\ahz{s}. The minimization algorithm~\cite{Anninos:1996ez} finds the local minimum of $\oint_S (\Theta - \Theta_o )^2 d^2S$ corresponding to a surface of constant expansion $\Theta_o$, with $\Theta_o=0$ corresponding to the \ahz{.} For time-symmetric data, the option exists to find instead the minimum of the surface area, which in this case corresponds to an \ahz{.} An alternative algorithm provided by -\codename{AHFinder}, the flow algorithm~\cite{Gundlach97a}, on +\codename{AHFinder}, the flow algorithm~\cite{Gundlach:1997us}, on which the above described \codename{EHFinder} is also based. Defining a surface as a level set $f(x^i)=r-h(\theta,\phi)=0$, and introducing an unphysical timelike parameter $\lambda$ to @@ -1256,7 +1256,7 @@ in the spacetime. The module \codename{ML_ADMQuantities} of the McLachlan code~\cite{McLachlan:web} uses the latter method, creating gridfunctions containing the integrand of the volume -integrals~\cite{Yo02a} +integrals~\cite{Yo:2002bm} \begin{eqnarray} M &=& \frac{1}{16\pi} \int_\Omega d^3 x \left[ e^{5 \phi} \left( 16 \pi \rho + \tilde{A}_{ij} \tilde{A}^{ij} - \frac23 K^2 @@ -1276,7 +1276,7 @@ $e^{6\phi} \epsilon_{ij}^k x^j \tilde{A}^\ell_k$ on the boundaries of the computational domain vanish. The ADM mass and angular momentum can also be calculated by the module \codename{Extract}, from the -variables stored in the base modules, as surface integrals~\cite{Bowen80} +variables stored in the base modules, as surface integrals~\cite{Bowen:1980yu} \begin{eqnarray} M &=& - \frac{1}{2\pi} \oint \tilde{D}^i \psi d^2 S_i \ J_i &=& \frac{1}{16\pi} \epsilon_{ijk} \oint \left( x^j K^{km} @@ -1310,11 +1310,11 @@ on Schwarzschild or calculation of the Weyl scalar $\Psi_4$.

The module \codename{Extract} uses the Moncrief formalism~\cite{ -Moncrief74} to extract, given spherical surfaces of constant coordinate +Moncrief:1974am} to extract, given spherical surfaces of constant coordinate radii, gauge-invariant wavefunctions $Q_{\ell m}^\times$ and $Q_{\ell m}^+$. The spatial metric is expressed as a perturbation on Schwarzschild and expanded onto a basis for tensors chosen here to be -the Regge-Wheeler harmonics~\cite{Regge57} described by six standard +the Regge-Wheeler harmonics~\cite{Regge:1957td} described by six standard Regge-Wheeler functions $\lbrace c_1^{\times\ell m}, c_2^{\times\ell m}, h_1^{+\ell m}, H_2^{+\ell m},K^{+\ell m}, G^{+ \ell m} \rbrace$. From these basis functions the gauge-invariant quantities