Surface layers in general relativity and their relation to surface tensions

For a thin shell, the intrinsic 3-pressure will be shown to be analogous to -A, whereA is the classical surface tension: First, interior and exterior Schwarzschild solutions will be matched together such that the surface layer generated at the common boundary has no gravitational mass; then its intrinsic 3-pressure represents a surface tension fulfilling Kelvin's relation between mean curvature and pressure difference in the Newtonian limit. Second, after a suitable definition of mean curvature, the general relativistic analog to Kelvin's relation will be proven to be contained in the equation of motion of the surface layer.