6. We present the combined system of elasticity and aging equations in section 7 and discuss special cases of the aging equations in section 8. Corresponding to the material and laboratory symmetries, we consider the space and material balance laws in section 9. In section 10 the Energy-Momentum balance Law and the decomposition of the Energy-Momentum tensor into components, including the Eshelby tensor and terms related to the aging processes are presented. In the final section we explore the application of this model to the basic inelastic processes- unconstrained aging, stress relaxation, and creep of a homogeneous rod.

4D kinematics of media with a variable metric.
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In this section we introduce the basic elements of the kinematics of a continuum with a variable metric, including material space-time $P$, 4D material metric $G$, 4D deformations $\phi$, slicing of the material space-time by the surfaces of constant physical time $B_{\phi ,t}$, and total, elastic and irreversible strain tensors.

Physical and Material Space-Time
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Let us consider the 4-D Euclidean vector space $M={\mathbb R}\times
{\mathbb R}^{3}$ ([**physical space-time**]{}) with the standard Euclidean metric $H$. There exists the volume form $d^{4}v$ corresponding to this metric.

We select global coordinates $x^{i},i=1,2,3,$ in the physical 