Metrics on End-Periodic Manifolds as Models for Dark Matter

TL;DR

This paper explores how end-periodic manifolds, used in exotic smooth structures of ^4, can generate metrics and matter models that may provide insights into dark matter distribution, supported by Einstein equations and energy condition analysis.

Contribution

It introduces a novel approach to modeling dark matter using exotic smooth structures on end-periodic manifolds, with explicit examples and physical viability assessments.

Findings

Three distinct matter models on end-periodic manifolds are constructed.

Some models satisfy the Einstein equations and energy conditions.

Comparison suggests potential of exotic smooth structures in dark matter modeling.

Abstract

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