<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','to olbar=no,location=no,scrollbars=yes,resizable=yes, status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usene t 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>Hi,\n\nOf the two ways that i\'m aware of to obtain the Einstein tensor, one\nas the double trace of the double dual of Riemann, the other as Ricci\nless half the trace, both seem to depend on a metric to go up and down\nsome of the indices. So im curious if there is an alternate, possibly\nobscure way to define Einstein that depends only on the connection.\n\nAlso, how is precisely defined the Cartan moment of rotation? from\nwhat i\'ve read is something like a delta position vector wedge net\nrotation of a vector around an infinitesimal loop? so this is\nesentially dP ^ riemann( dx ^ dy ). This gives a 3-vector. So then one\nequates this Cartan moment of rotation with currents of matter\nenergy-momentum densities and defines Einstein as the divergence of\nthis moment of rotation?\n\nAnyway, the above computation of moment of rotation is based on what a\nlooptrip does to a vector. I still haven\'t found an exposition that\ncomputes the variation of a (non-vector)
tensor around a loop. I can\nwildguess that one must add a Riemann term for each index in the tensor\nwith a sign depending of the index level but i would like to be\ncorrected if im wrong. So one would think that a Cartan moment of\nrotation defined as above is valid only for vector quantities\nrotations. Is this correct?\n\n\nCheers,\n\nCharles J. Quarra\n\n\n\n\n---------------------------------\nA tu celular ¿no le falta algo?\nUsá Yahoo! Messenger y Correo Yahoo! en tu teléfono celular.\nMás información aquí.\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>Hi,
Of the two ways that i'm aware of to obtain the Einstein tensor, one
as the double trace of the double dual of Riemann, the other as Ricci
less half the trace, both seem to depend on a metric to go up and down
some of the indices. So im curious if there is an alternate, possibly
obscure way to define Einstein that depends only on the connection.
Also, how is precisely defined the Cartan moment of rotation? from
what i've read is something like
position vector wedge net
rotation of a vector around an infinitesimal loop? so this is
esentially
riemann(
. This gives a 3-vector. So then one
equates this Cartan moment of rotation with currents of matter
energy-momentum densities and defines Einstein as the divergence of
this moment of rotation?
Anyway, the above computation of moment of rotation is based on what a
looptrip does to a vector. I still haven't found an exposition that
computes the variation of a (non-vector) tensor around a loop. I can
wildguess that one must add a Riemann term for each index in the tensor
with a sign depending of the index level but i would like to be
corrected if im wrong. So one would think that a Cartan moment of
rotation defined as above is valid only for vector quantities
rotations. Is this correct?
Cheers,
Charles J. Quarra
---------------------------------
A tu celular ¿no le falta algo?
Usá Yahoo! Messenger y Correo Yahoo! en tu teléfono celular.
Más información aquí.
