There is a great resume on dynamics of thin shells in GR: Berezin87: Dynamics of bubbles in GR (Phys. Rev. D 36, 2919) In section III/A above the equation (3.1) there is the following statement: "Thus, for given inner and outer metrics sigma determine the global geometry (i.e. how the inner geometry is stuck together to the outer one)" Sigma is a sign +1 or -1, see for example in the master equation (Schwarzschild-Schwarzschild thin shell): sigma_in*sqrt(1-2mc/r+v^2) - sigma_out*sqrt(1-2(mc+mg)/r+v^2) = mr/r where r is the circumferential radius; v = dr/dtau, and tau is the proper time of the shell; mc is the central Schwarzschild mass parameter; mg is the gravitational mass of the shell, this means that the outer Schwarzschild mass parameter is mc+mg; and mr is the rest mass of the shell, mr > 0; It can be shown for all four possibilities of the signs that the following equation of motion can be derived independent of the signs: (dr/dtau)^2 = (mg/mr)^2 - 1 + (2mc+mg)/r + (mr/2r)^2 This coincide with the above statement, because he signs do not influence the local motion. But in another paper of Goldwirth & Katz: http://arxiv.org/abs/gr-qc/9408034 they have a nice illustration of gluing manifolds together: http://arxiv.org/PS_cache/gr-qc/ps/9408/9408034v3.fig1-1.png [Broken] They suggest that the signs comes from the four possibilities: witch half of the manifolds is chosen. But if we have already chosen the half, we also fix the metric. I think Berezin's statement means that the signs comes from how to join chosen metrics together, and not how to chose the metrics!