This article is a review of what could be considered the basic mathematics of Einstein–
Cartan theory. We discuss the formalism of principal bundles, principal connections …

We describe the Hamilton geometry of the phase space of particles whose motion is
characterized by general dispersion relations. In this framework spacetime and momentum …

Physical foundations for relativistic spacetimes are revisited in order to check at what extent
Finsler spacetimes lie in their framework. Arguments based on inertial observers (as in the …

A theory of gravity is deduced from the axioms of the premetric program. The starting point is
the conservation of energy and momenta, and the equivalence of gravitation and inertia. The …

We propose a new model for the description of a gravitating multiparticle system, viewed as
a kinetic gas. The properties of the (colliding or noncolliding) particles are encoded into a so …

A novel first-order action principle has been proposed as the possible foundation for a more
fundamental theory of general relativity and the Standard Model. It is shown in this article …

We introduce a definition of symmetry generating vector fields on manifolds which are
equipped with a first-order reductive Cartan geometry. We apply this definition to a number …

A Cartan geometry of the General Linear symmetry is formulated by dividing out the
displacements from the group. The resulting action is quadratic in curvature, polynomial in …

A theory of gravity is deduced from the axioms of the premetric program. The starting point is
the conservation of energy and momenta, and the equivalence of gravitation and inertia. The …

Black hole solutions are explored in the Lorentz gauge theory of gravity. The fields of the
theory are the gauge potential in the adjoint and a scalar in the fundamental representation …