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Metric problem

  1. Nov 20, 2009 #1
    the metric is [tex]ds^2=f(x,y)(dx^2+dy^2)+dz^2-dt^2[/tex]

    [tex]G_{tt}=-G_{zz}=-\frac{1}{2f(x,y)}\nabla^2(ln(f(x,y)))[/tex]

    the energy moment is
    [tex]T_{tt}=\delta(x)\delta(y)\frac{A}{f(x,y)}=-T_{zz}[/tex]

    as I calculate f(x,y)?

    i tried:
    [tex]g(x,y)=ln(f(x,y))[/tex]and using [tex]G_{tt}=kT_{tt}[/tex]
    [tex]\frac{dg^2}{dx^2}+\frac{dg^2}{dy^2}=kA\delta(y)\delta(x)[/tex]....A konstant

    but, do not find it.......


    the result is [tex]ds^2= r^{-u}(dr^2+r^2d\phi^2)+dz^2-dt^2[/tex]

    where obviously [tex]dr^2+r^2d\phi^2= dx^2+dy^2[/tex]
    [tex]r^2=x^2+y^2[/tex]
    [tex]u=konstant*A[/tex]
     
  2. jcsd
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