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If you have a classical field like the Higgs that is initially in an unstable equilbrium, then it can make a transition to a stable equilibrium and release energy. What I don't understand is the effect of this transition on gravity (or spacetime curvature). The transition converts a kind of potential energy in the field to active energy in the form of heat. But in GR, potential energy curves spacetime just as other kinds of energy does. So would such a transition have an effect on spacetime curvature at all?