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Putting the GR math aside for just one second, have you ever wondered what gravitation really is?
From the moment you hit gauss's [negative] divergence, it really makes you stop and think, what's dragging the spacetime carpet into the cellar, furniture and all, and without effort? Is the continuum energy being consumed, like water down a drain, taking the soap bubbles with it?
What I also find remarkable, is that it takes a force to alter the speed or direction of a massed object in uniform motion or at rest, right?! So, if gravitation offers force free acceleration by pulling spacetime in, towards mass - from a solitary electron to a black hole - then what's doing the pulling, what's doing the bending and warping as another massed object, in force free uniform motion, cruises along its Geodesic, and bends around the massed body? Also, the concept that laws are 'universal', seems to stop right there, since laws are carried alongside the Christoffels (representing the forces) and are not carried across spacetime. Remember this is where Einstein's 'get out of jail free' card came into play, he said that the notion of an absolute space or absolute time, for SR and GR, must be abolished, which was right after he used just that notion, a "Local Time" to formulate SR in the first place (Clock Synchronization, as per Lorentz and FitzGerald 's interpretation of Michelson and Morley's 1887 experiment). Seriously, it's the [Minkowski] dog chasing its own tail (did you like my little Polytechnikum joke there?).
We all know that spacetime is drawn toward the presence of mass, but how does spacetime know it is there, how much is there, and the density, which in turn affects the rate at which spacetime is pulled (metric value)?
Seriously, it's almost as though mass is a heatsink for energy. I can't bring myself to believe in either the Higgs Field or Particle, and would happily put a 100 pound bet that the LHC doesn't find it (Stephen Hawking style).
Sorry to interrupt your Gij's and Gji's (Riemann's equality was it?)
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