York's Initial Data [Archive]

David Norton

Jun30-04, 05:38 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>I hope this is the right place to ask this question. At the moment I\'m\nlearning about the various ways one can formulate general relativity as\nan initial value problem. I understand the standard ADM method, but I\'m\nhaving some trouble with York\'s conformal approach. Does anyone know of\nany examples where York\'s conformal method is worked through in detail,\npreferably with examples?\n\nI\'ve tried googling, but haven\'t found anything which works through the\nsteps in sufficient detail. Something which started with an initial\ndata set and then works through finding the conformal factor from the\nHamiltonian constraint would be perfect.\n\nThanks in advance.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>I hope this is the right place to ask this question. At the moment I'm
learning about the various ways one can formulate general relativity as
an initial value problem. I understand the standard ADM method, but I'm
having some trouble with York's conformal approach. Does anyone know of
any examples where York's conformal method is worked through in detail,
preferably with examples?

I've tried googling, but haven't found anything which works through the
steps in sufficient detail. Something which started with an initial
data set and then works through finding the conformal factor from the
Hamiltonian constraint would be perfect.

Thanks in advance.

Charles Torre

Jul1-04, 04:48 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"David Norton" <david_norton80@yahoo.co.uk> wrote in message news:<cbq7fm\\$mks@odah37.prod.google.com>...\n> I hope this is the right place to ask this question. At the moment I\'m\n> learning about the various ways one can formulate general relativity as\n> an initial value problem. I understand the standard ADM method, but I\'m\n> having some trouble with York\'s conformal approach. Does anyone know of\n> any examples where York\'s conformal method is worked through in detail,\n> preferably with examples?\n>\n> I\'ve tried googling, but haven\'t found anything which works through the\n> steps in sufficient detail. Something which started with an initial\n> data set and then works through finding the conformal factor from the\n> Hamiltonian constraint would be perfect.\n>\n\nHave you had a look at Greg Cook\'s review? It\'s at\n\nhttp://relativity.livingreviews.org/Articles/lrr-2000-5/index.html\n\nHe explains the formalism, works through some important examples,\nand gives pointers to the literature.\n\ncharlie torre\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>"David Norton" <david_norton80@yahoo.co.uk> wrote in message news:<cbq7fm$mks@odah37.prod.google.com>...
> I hope this is the right place to ask this question. At the moment I'm
> learning about the various ways one can formulate general relativity as
> an initial value problem. I understand the standard ADM method, but I'm
> having some trouble with York's conformal approach. Does anyone know of
> any examples where York's conformal method is worked through in detail,
> preferably with examples?
>
> I've tried googling, but haven't found anything which works through the
> steps in sufficient detail. Something which started with an initial
> data set and then works through finding the conformal factor from the
> Hamiltonian constraint would be perfect.
>

Have you had a look at Greg Cook's review? It's at

http://relativity.livingreviews.org/Articles/lrr-2000-5/index.html

He explains the formalism, works through some important examples,
and gives pointers to the literature.

charlie torre

Jonathan Thornburg

Jul2-04, 04:32 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nDavid Norton <david_norton80@yahoo.co.uk> wrote:\n> I understand the standard ADM method, but I\'m\n> having some trouble with York\'s conformal approach. Does anyone know of\n> any examples where York\'s conformal method is worked through in detail,\n> preferably with examples?\n\nNumerical calculations in general relativity often use the York-\nLichnerowicz conformal approach. The standard reference on the theory\nside would be York\'s paper\n\n@incollection{York79,\nkey = {York79},\nX-author = "James W. York, Jr.",\nauthor = "York, Jr., James W.",\ntitle = "Kinematics and Dynamics of General Relativity",\npages = "83--126",\neditor = "Larry L. Smarr",\nbooktitle = "Sources of Gravitational Radiation",\npublisher = "Cambridge University Press",\naddress = "Cambridge, UK",\nyear = 1979,\nisbn = "0-521-22778-X",\nsnote = "Proceedings of the Battelle Seattle Workshop,\n24 July -- 4 August, 1978",\n}\n\nAs to someone working through in detail how it\'s used, there are\nlots of numerical papers. Greg Cook has a review talk on the web,\nhttp://www.ima.umn.edu/talks/workshops/6-24-29.2002/cook/IMAidrev.pdf\nand he has a long review paper at\nhttp://www.livingreviews.org/Articles/Volume3/2000-5cook\n\nciao,\n\n--\n-- "Jonathan Thornburg (remove -animal to reply)" <jthorn@aei.mpg-zebra.de>\nMax-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut),\nGolm, Germany, "Old Europe" http://www.aei.mpg.de/~jthorn/home.html\n"Washing one\'s hands of the conflict between the powerful and the\npowerless means to side with the powerful, not to be neutral."\n-- quote by Freire / poster by Oxfam\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>David Norton <david_norton80@yahoo.co.uk> wrote:
> I understand the standard ADM method, but I'm
> having some trouble with York's conformal approach. Does anyone know of
> any examples where York's conformal method is worked through in detail,
> preferably with examples?

Numerical calculations in general relativity often use the York-
Lichnerowicz conformal approach. The standard reference on the theory
side would be York's paper

@incollection{York79,
key = {York79},
X-author = "James W. York, Jr.",
author = "York, Jr., James W.",
title = "Kinematics and Dynamics of General Relativity",
pages = "83--126",
editor = "Larry L. Smarr",
booktitle = "Sources of Gravitational Radiation",
publisher = "Cambridge University Press",
address = "Cambridge, UK",
year = 1979,
isbn = "0-521-22778-X",
snote = "Proceedings of the Battelle Seattle Workshop,
24 July -- 4 August, 1978",
}

As to someone working through in detail how it's used, there are
lots of numerical papers. Greg Cook has a review talk on the web,
http://www.ima.umn.edu/talks/workshops/6-24-29.2002/cook/IMAidrev.pdf
and he has a long review paper at
http://www.livingreviews.org/Articles/Volume3/2000-5cook

ciao,

--
-- "Jonathan Thornburg (remove -animal to reply)" <jthorn@aei.mpg-zebra.de>
Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut),
Golm, Germany, "Old Europe" http://www.aei.mpg.de/~jthorn/home.html
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam