In this paper we develop the complete theory of the relativistic motion of a singular layer of matter under the influence of surface tension and volume tension. In order to account for vacuum tension effects we suggest a formalism of universal applicability: the single degree of freedom of a relativistic ‘‘bubble’’ is coupled in a gauge-invariant manner to a potential three-form A in the presence of gravity. The mathematical and physical consequences of this coupling can be summarized as follows. (i) The action functional of the theory, when written in geometric form, is formally quite similar to the Einstein-Maxwell action for the dynamics of a point charge on a Riemannian manifold. However, in comparison with electrodynamics, bubble dynamics is a highly constrained theory with a vastly different physical content: the gauge field F=dA propagates no degrees of freedom and when it is coupled to gravity alone, it gives rise to a cosmological constant of arbitrary magnitude.
