From: patzermike.mc@gmail.com   
      
   I have been exploring a fun GR problem.  Consider a uniform planar   
   mass distribution in the xy plane.  The spacetime metric will only   
   depend on z.  An elementary argument shows that the metric has the   
   form g_xx = g_yy = A(z), g_zz = B(z), and g_tt = -C(t).  By a change   
   of the z coordinate one can simplify by setting B(z) = 1.  It is   
   not a hard exercise to work out the Ricci tensor, set it equal to   
   0, and solve for the functions A and C.  The derivation is similar   
   to but somewhat simpler than the derivation of the Schwartzchild   
   metric.  The metric is singular in the xy plane and there is an   
   analogue of the Schwartzchild radius.   
      
   I am trying to come up with a model for a slab of matter that exists   
   for -h < z < h.  Does anyone have thoughts for a physically realistic   
   stress energy tensor that would describe, say, an infinite planar   
   slab of gravitating fluid.  Perhaps it is absurd to use the phrase   
   "physically realistic" for this math exercise, but I find the problem   
   interesting.  There are a couple papers on the idealized massive   
   plane of thickness 0, but not many.   After all, nature doesn't   
   present us with infinite massive planes.  But anyways, what would   
   be a suitable stress energy tensor for a thick slab?   
      
   --- SoupGate-Win32 v1.05   
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