Does general relativity highlight necessary connections in nature?

Real-polynomial formulation of general relativity in terms of connections.

I show in this letter that it is possible to construct a Hamiltonian description for Lorentzian General Relativity in terms of two real SO(3) connections. The constraints are simple polynomials in the basic variables. The present framework gives us a new formulation of General Relativity that keeps some of the interesting features of the Ashtekar formulation without the complications associated...

Nonlinear Connections and Nearly Autoparallel Maps in General Relativity

We apply the method of moving anholonomic frames, with associated nonlinear connections, in (pseudo) Riemannian spaces and examine the conditions when various types of locally anisotropic (la) structures (Lagrange, Finsler like and more general ones) could be modeled in general relativity. New classes of solutions of the Einstein equations with generic local anisotropy are constructed. We formu...

Necessary and sufficient condition for hydrostatic equilibrium in general relativity

We present explicit examples to show that the ‘compatibility criterion’ [recently obtained by us towards providing equilibrium configurations compatible with the structure of general relativity] which states that: for a given value of σ[≡ (P0/E0) ≡ the ratio of central pressure to central energy-density], the compactness ratio u[≡ (M/R), whereM is the total mass andR is the radius of the config...

Does Nature Prefer Heterocycles?

The Field Nature of Time in General Relativity

The paper is devoted to the description of the reparametrization invariant dynamics of general relativity obtained by resolving constraints and constructing equivalent unconstrained systems. The constraint-shell action reveals the ”field nature” of the geometric time in general relativity. The time measured by the watch of an observer coincides with one of field variables, but not with the repa...