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John Schutkeker
Jan26-06, 06:31 PM
Christophe <chatelai@club-internet.fr> wrote in news:dnjnin$ak4$1
@arcturus.ciril.fr:

> I recently tried to understand general relativity. Basically, I have
> seen how can one construct from the action principle the equations of
> motion of particles or classical fields and the equations of motion of
> the curvature of the space-time (Einstein equations). I was wondering
> how to do statistical physics within this framework. Can one write the
> Boltzmann joint probability distribution of the particles (x,p) and the
> metric g of the space-time as something like
>
> P(x,p,g) = exp(-beta (T_00 + t_00))
>
> where beta=1/kT, T_00 stands for the energy density of the particles and
> t_00 of the space-time (in the linear regime g=\eta+h ?!) ?
>
> If you have some (not too technical) references to suggest...

You're posting in the wrong group. Sci.physics is much more heavily
travelled, and you're much more likely to find a knowledgeable contact in
there.

To my naive ear, this sounds like Hawking radiation and/or quantum foam.
Those are probably the areas where you should look for references on the
overlap between thermal physics and general realtivity. Sorry I can't name
a textbook, but I'll wager $10 that somebody in sci.physics can.

The library call letters for general relativity are QC 173.6 and for
statistical physics, they are QC 174.8. You should visit the best library
you can find and go digging through these areas of the shelves, looking for
the newest books available.

tessel@um.bot
Jan26-06, 06:35 PM
Christophe <chatelai@club-internet.fr> wrote:

> I recently tried to understand general relativity. Basically, I have
> seen how can one construct from the action principle the equations of
> motion of particles or classical fields and the equations of motion of
> the curvature of the space-time (Einstein equations). I was wondering
> how to do statistical physics within this framework. Can one write the
> Boltzmann joint probability distribution of the particles (x,p) and the
> metric g of the space-time

Not sure I understand what you are looking for, but if you just want to
study the Boltzmann equation in the context of gtr, as it happens
Einstein-Boltzmann solutions are all the rage just now! See the excellent
review article

http://relativity.livingreviews.org/Articles/lrr-2005-2/index.html

T. Essel