David Park
May25-04, 01:29 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>Can anybody help me understand the calculation of the geodesic effect as\npresented in Section 4.7 of the Foster & Nightingale text "A Short Course in\nGeneral Relativity"?\n\nI can reproduce all of the calculations in the section and obtain a facile\nunderstanding, but have trouble with interpretation and details that are\nrather finessed by the authors.\n\nIn the opening paragraph they state: "The orthogonality condition simply\nmeans that lamba^mu has no temporal component in an instantaneous rest frame\nof an observer traveling along the geodesic."\n\nBut later we see that lambda^0 is a constant times lambda^3, which is not\nzero. So is the above statement only true in flat spacetime, or is the frame\nthat the lambda vector is expressed in not the instantaneous rest frame of\nthe observer traveling along the geodesic?\n\nAlso, when I try to calculate the length of the lamda vector using the\nSchwarzschild metric I do not obtain a constant value. Sould I\ncalculate -ds^2 with a nonzero lambda^0 component or should I simply\ncalculate the spatial part using lamda^1 to lamda^3? In either case the\nlength is not constant.\n\nDavid Park\ndjmp@earthlink.net\nhttp://home.earthlink.net/~djmp/\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>Can anybody help me understand the calculation of the geodesic effect as
presented in Section 4.7 of the Foster & Nightingale text "A Short Course in
General Relativity"?
I can reproduce all of the calculations in the section and obtain a facile
understanding, but have trouble with interpretation and details that are
rather finessed by the authors.
In the opening paragraph they state: "The orthogonality condition simply
means that lamba^\mu has no temporal component in an instantaneous rest frame
of an observer traveling along the geodesic."
But later we see that \lambda^0 is a constant times \lambda^3, which is not
zero. So is the above statement only true in flat spacetime, or is the frame
that the \lambda vector is expressed in not the instantaneous rest frame of
the observer traveling along the geodesic?
Also, when I try to calculate the length of the lamda vector using the
Schwarzschild metric I do not obtain a constant value. Sould I
calculate -ds^2 with a nonzero \lambda^0 component or should I simply
calculate the spatial part using lamda^1 to lamda^3? In either case the
length is not constant.
David Park
djmp@earthlink.net
http://home.earthlink.net/~djmp/
presented in Section 4.7 of the Foster & Nightingale text "A Short Course in
General Relativity"?
I can reproduce all of the calculations in the section and obtain a facile
understanding, but have trouble with interpretation and details that are
rather finessed by the authors.
In the opening paragraph they state: "The orthogonality condition simply
means that lamba^\mu has no temporal component in an instantaneous rest frame
of an observer traveling along the geodesic."
But later we see that \lambda^0 is a constant times \lambda^3, which is not
zero. So is the above statement only true in flat spacetime, or is the frame
that the \lambda vector is expressed in not the instantaneous rest frame of
the observer traveling along the geodesic?
Also, when I try to calculate the length of the lamda vector using the
Schwarzschild metric I do not obtain a constant value. Sould I
calculate -ds^2 with a nonzero \lambda^0 component or should I simply
calculate the spatial part using lamda^1 to lamda^3? In either case the
length is not constant.
David Park
djmp@earthlink.net
http://home.earthlink.net/~djmp/