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In this paper we will detail an approach to generate metrics and mattermodels on end-periodic manifolds, which are used extensively in the study ofthe exotic smooth structures of $\mathbb{R}^4$. We will present three distinctexamples, discuss their associated matter models by solving the Einsteinequations, and determine their physical viability by examining the energyconditions. We will also compare one of the models directly with existingmodels of matter distributions in extragalactic systems, to highlight theviability of utilizing exotic smooth structures to understand the existence anddistribution of dark matter.

Metrics on End-Periodic Manifolds as Models for Dark Matter