From: fortunati.luigi@gmail.com   
      
   Gravity is a force and, therefore, is a vector.   
      
   Is spacetime curvature a vector? Does it have a direction and a verse?   
      
   Luigi Fortunati   
      
   [[Mod. note --   
   In order to answer questions like this, we need to be precise in   
   our terms.  You write that "Gravity is a force".  But what do you mean   
   by "gravity"?  Starting with Newtonian mechanics for simplicity,   
   "gravity" could plausibly mean any of several things:   
   * gravitational potential energy (which is a scalar in Newtonian mechanics).   
   * the Newtonian "little g" (which is a 3-vector at any given position   
     and time   
   * the *difference* in the Newtonian "little g" between nearby objects   
     at a given time; this difference is what you can measure about the   
     gravitational field if you're in a freely falling elevator.  This   
     difference is a 3-vector which depends on the separation between the   
     nearby objects,   
       difference = M * separation   
     where M is a 3x3 matrix and "*" denotes matrix multiplication.  This   
     3x3 matrix M (which is really a rank 2 tensor) provides a complete   
     description of the local gravitational field at a given position and   
     time.   
      
   In general relativity (GR) things are (not surprisingly) more complicated.   
   To fully describe spacetime curvature at an event (a point in space, at   
   a particular time) requires generalizing the 3x3 matrix (rank 2 tensor) M   
   to the Riemann curvature tensor, which is a 4x4x4x4 4-dimensional matrix   
   (really a rank 4 tensor), i.e., it's a set of 4x4x4x4 = 256 numbers.   
   The Riemann curvature tensor has a bunch of symmetries, so it actually   
   has only 20 independent components.   
      
   So in GR, the best answer to your question is that spacetime curvature "is"   
   the Riemann curvature tensor.  This doesn't have a single "direction" any   
   more than the 3x3 matrix M has a "direction" in Newtonian mechanics.   
   -- jt]]   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)