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arXiv · 1508.07765

Curved space-times by crystallization of liquid fiber bundles

Frédéric Hélein·Dimitri Vey
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Abstract

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.

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Frédéric Hélein, Dimitri Vey. 2015-08-31. Curved space-times by crystallization of liquid fiber bundles. https://doi.org/10.1007/s10701-016-0039-2

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