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We extend the superconductor's free energy to include an interaction of theorder parameter with the curvature of space-time. This interaction leads togeometry dependent coherence length and Ginzburg-Landau parameter whichsuggests that the curvature of space-time can change the superconductor's type.The curvature of space-time doesn't affect the ideal diamagnetism of thesuperconductor but acts as chemical potential. In a particular circumstance,the geometric field becomes order-parameter dependent, therefore thesuperconductor's order parameter dynamics affects the curvature of space-timeand electrical or internal quantum mechanical energy can be channelled into thecurvature of space-time. Experimental consequences are discussed.

The Geometric Field (Gravity) as an Electro-Chemical Potential in a Ginzburg-Landau Theory of Superconductivity