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Re: non-linear gravitational wave solution

Hello Mario,

Sunday, April 09, 2000, 6:31:58 PM, you wrote:

MD> --Boundary_(ID_2lG+2v+CONjgGgqVNRExcw)
MD> Content-type: text/plain; charset=us-ascii

MD> lutjmail wrote:

Can someone please tell me about the directly solution
of non-linear equation R_uv=0, where R_uv is the Ricci tensor. There is
no weak field condition in this equation.

I want to know the answer or the reference papers or books.


MD> R_uv=0 is a whole family of solutions. They're called vacuum solutions
MD> because they give the set of solutions of Einstein's eq. of gravitation
MD> that correspond to a region of spacetime without matter sources.
MD> They're highly non-linear and coupled and in 3+1 dimensions they're a set
MD> of 10 eqs (16 but in symmetric gravity they reduced to 10).
MD> To get introduced to the field:
MD> Schutz, B.F. (1980) A first course in general gravity. Cambridge U.P.
MD> More advanced:
MD> Wald. R. (1982) General Relativity The U. of Chicago P.
MD> The reference cited by somebody else Exact Sol. of Einstein's Field
MD> Equations is a good technical reference to both solutions with the Ricci
MD> tensor = 0 and with matter content (Ricci nonzero).
MD> cheers,
MD> mario

MD> --
MD> ***************************************************************
MD> Mario Diaz
MD> Associate Professor of Physics-Department of Physical Sciences
MD> Interim Chair - Department of Engineering Technology
MD> University of Texas at Brownsville
MD> mdiaz@utb1.utb.edu Voice:956-5746641 FAX: (956) 574-6692
MD> http://utopia.utb.edu/mario
MD> ***************************************************************



MD> --Boundary_(ID_2lG+2v+CONjgGgqVNRExcw)
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MD> <!doctype html public "-//w3c//dtd html 4.0 transitional//en">
MD> <html>
MD> lutjmail wrote:
MD> <blockquote TYPE=CITE>Can someone please tell me about the directly solution
MD> <br>of non-linear equation R_uv=0, where R_uv is the Ricci tensor. There
MD> is
MD> <br>no weak field condition in this equation.
MD> <p>I want to know the answer or the reference papers or books.
MD> <br>&nbsp;</blockquote>
MD> R_uv=0 is a whole family of solutions. They're called vacuum solutions
MD> because they give the set of solutions of Einstein's eq. of gravitation
MD> that correspond to&nbsp; a region of spacetime without matter sources.
MD> <br>They're highly non-linear and coupled and in 3+1 dimensions they're
MD> a set of 10 eqs (16 but in symmetric gravity they reduced to 10).
MD> <br>To get introduced to the field:<br>
MD> Schutz, B.F. (1980) A first course in general gravity. Cambridge U.P.
MD> <br>More advanced:
MD> <br>Wald. R. (1982) General Relativity The U. of Chicago P.
MD> <br>The reference cited by somebody else Exact Sol. of Einstein's Field
MD> Equations is a good technical reference to both solutions with the Ricci&nbsp;
MD> tensor = 0 and with matter content (Ricci nonzero).
MD> <br>cheers,
MD> <br>mario
MD> <pre>--&nbsp;
MD> ***************************************************************
MD> Mario Diaz&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
MD> Associate Professor of Physics-Department of Physical Sciences
MD> Interim Chair - Department of Engineering Technology&nbsp;
MD> University of Texas at Brownsville
MD> mdiaz@utb1.utb.edu&nbsp;&nbsp;&nbsp; Voice:956-5746641&nbsp;&nbsp;&nbsp; FAX: (956) 574-6692
MD> <A HREF="http://utopia.utb.edu/mario";>http://utopia.utb.edu/mario</A>
MD> ***************************************************************</pre>
MD> &nbsp;</html>

MD> --Boundary_(ID_2lG+2v+CONjgGgqVNRExcw)--


Thank you for tell me the books related to my question. I borrowed
all of them today. I found the solutions are analytic. what I want to
try is to found out the numeric solution of the R_{uv}=0, and check
if the solution could be a soliton or a nonlinear wave packet.
I think the deep nonlinear equation could not have an analytic
solution. May be my thought is not applicable, but I want try.
May be some one can give me some information that if some physicians
have done such kind of work.

--
Best regards,
Qiang mailto:luqiang@tjmail.com