This is really a continuation from another thread but will start here from scratch. Consider the case of a static thin spherical mass shell - outer radius rb, inner radius ra, and (rb-ra)/ra<< 1, and with gravitational radius rs<< r(shell). According to majority opinion at least, in GR the exterior spacetime for any r >= rb is that given by SM (Schwarzschild metric) as expressed by the SC's (Schwarzschild coordinates) http://en.wikipedia.org/wiki/Schwarzschild_metric#The_Schwarzschild_metric. In the empty interior region r=< ra, a flat MM (Minkowski metric) applies. Owing probably to it's purely scalar nature, there seems little controversy as to the temporal component transition, as expressed as frequency redshift scale factor Sf = f'/f (f' the gravitationally depressed value as seen 'at infinity'). In terms of the potential V = (1-rs/r)1/2, with rs = 2GMc-2, one simply has Sf = V, which for any r=< ra has it's r parameter value 'frozen' at r = ra. There is a smooth transition from rb to ra that depends simply on V only. So far, so broadly reasonable. What of the spatial metric components? In terms of corresponding scale factors Sr, St that operate on the radial and tangent spatial components respectively, it is readily found from the SC's that Sr = V, St = 1, everywhere in the exterior SM region. Sr = V is physically reasonable and identical to frequency redshift factor Sf here. Whether according to GR Sf and Sr diverge for some reason in the transition to the interior MM region is not clear to me, but that would be 'interesting'. An apparently consensus view that St dives relatively steeply from St = 1 at r = rb, to some scaled fraction of V at r=< ra. [A previous attempt here at PF at the shell transition problem found something different; an invariant St = 1 for all r, but an Sr that jumped back from V to 1 in going from rb to ra. That gave flat interior spatial metric with unity scale factors Sr, St (i.e. 'at infinity' values) but a redshift factor Sf = V]. Seems though the consensus view is for an equally depressed Sr, St in the interior MM region, the exact value of Sr, St, and Sf relative to V is unclear from recent entries on that matter, where parameters A, B, were used as equivalent to Sf, (Sr, St) respectively. I wish to focus on the question of physical justification for St diving from unity to some fraction of V. Given that an invariant St = 1 for all r >= rb (SM regime) stipulates complete independence on V or any combination of it's spatial derivatives ∂V/∂r, ∂2V/∂r2, etc. In the shell wall region, where shrinkage of St apparently occurs, there is owing to a nonzero stress-energy tensor T a different relative weighting of V and all it's derivatives to that applying for r => rb, but otherwise, only the weighting factors are different. What permits variance of St in one case, but not the other? An answer was that in the shell wall where T is nonzero, the Einstein tensor G (http://en.wikipedia.org/wiki/Einstein_tensor) operates and this is the explanation. That seems unsatisfying, and should be justifiable at a basic, 'bare kernel' level. By that is meant identify the 'primitives' from which everything in G can be derived, and show what particular combo leads to a physically justifiable variance of St, applying nowhere but the shell wall region. So what are the 'primitives'. I would say just V and it's spatial derivatives, which owing to the spherical symmetry, are of themselves purely radial vector quantities (but obviously not all their combinations as per div, curl etc). One caveat here is to nail down the relevant source of V - taken simply as total mass M exterior to rb. Has been pointed out that for a stable shell there must be pressure p present in addition to just rest matter density ρ, ie T = ρ + p, = T00 + T11+T22+T33. My assumption is that for a mechanically stable thin shell of normal material, ρ >>> p, and so to a very good approximation, just use ρ. If one feels the p terms should be included regardless, then I would further suggest they will act here just as a tiny addition to ρ. That is, the contribution of T11 for instance in some element of stressed matter introduces no 'directionality' per se to the potential, yes? Can't think of any physical quantity - relevant to this case anyway - that could not be expressed as some function of the above primitives. But recall, all these primitives exist in the region exterior to rb, where St is strictly = 1!. Only remotely relevant quantity I can think of that *may* be zero in the exterior region but obviously nonzero in the wall region is the three divergence nabla2V. And that could account for a varying St? Can't imagine how. So something real, real special has to be pulled out of the hat imo. So special I consider it impossible, but open to be shown otherwise. Seems to me the anomaly is intractable in GR and a cure requires a theory where isotropic contraction of spatial and temporal components apply. Then and only then the transition issue naturally resolves. But that's my opinion. So, any GR pro willing to give this a go, let's get on with the show!