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{-1 + (2*M)/r + \[Chi]^2*(-2*(1 - (2*M)/r)*(M^4/(r^3*(-2*M + r)) + 
      (M^3*(M + r)*(-1 + 3*Cos[\[Theta]]^2))/(2*r^4)) + 
    (4*M^4*Sin[\[Theta]]^2)/r^4), (1 - (2*M)/r)^(-1) + 
  (2*\[Chi]^2*(M^4/((2*M - r)*r^3) - 
     ((-5*M^4 + M^3*r)*(-1 + 3*Cos[\[Theta]]^2))/(2*r^4)))/(1 - (2*M)/r), 
 r^2 + \[Chi]^2*((M^3*(1 - 3*Cos[\[Theta]]^2))/r - 
    (M^4*(1 + 3*Cos[2*\[Theta]]))/r^2), r^2*Sin[\[Theta]]^2 + 
  \[Chi]^2*(-((M^3*(-1 + 3*Cos[\[Theta]]^2)*Sin[\[Theta]]^2)/r) - 
    (M^4*(1 + 3*Cos[2*\[Theta]])*Sin[\[Theta]]^2)/r^2), 
 (-2*M^2*\[Chi]*Sin[\[Theta]]^2)/r}
