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