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Motivated by the search for a Hamiltonian formulation of Einstein equationsof gravity which depends in a minimal way on choices of coordinates, nor on achoice of gauge, we develop a multisymplectic formulation on the total space ofthe principal bundle of orthonormal frames on the 4-dimensional space-time.This leads quite naturally to a new theory which takes place on 10-dimensionalmanifolds. The fields are pairs of $((\alpha,\omega),\varpi)$, where$(\alpha,\omega)$ is a 1-form with coefficients in the Lie algebra of thePoincar\'e group and $\varpi$ is an 8-form with coefficients in the dual ofthis Lie algebra. The dynamical equations derive from a simple variationalprinciple and imply that the 10-dimensional manifold looks locally like thetotal space of a fiber bundle over a 4-dimensional base manifold. Moreover thisbase manifold inherits a metric and a connection which are solutions of asystem of Einstein--Cartan equations.

Curved space-times by crystallization of liquid fiber bundles