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We interpret the exact solutions previously obtained for sphericallysymmetric shells of liquid fluid in General Relativity in terms of the energiesinvolved. We show that a certain parameter that was introduced into thesolutions by the interface boundary conditions is related to the bindingenergies of the gravitational systems. We then use this fact in order todiscuss the energetic stability of those solutions.  We include in the stability discussion the well-known interior Schwarzschildsolution for a liquid sphere, which can be obtained as a specific limit of thesolutions that we previously obtained for the liquid shells. We show that thissolution turns out to be a maximally unstable one, from the energetic point ofview discussed here.  We also perform a numerical exploration of the energetic stability criterionof the solutions, and show that indeed there is a particular subset of thesolutions which are energetically stable. All these solutions have the form ofshells with non-vanishing internal radii. This reduces the originalthree-parameter family of solutions to a two-parameter family of energeticallystable solutions.

Energetic Stability of the Solutions of the Einstein Field Equations for Spherically Symmetric Liquid Shells