Perfect Fluid Dark Matter

TL;DR

This paper models galactic dark matter as a perfect fluid within general relativity, linking flat rotation curves to the universe's background geometry and deriving dark matter properties.

Contribution

It derives a spacetime metric for galactic halos based on flat rotation curves, connecting dark matter distribution with the universe's geometry in a novel way.

Findings

Dark matter modeled as perfect fluid in galactic halos.

The resulting spacetime suggests a nearly flat universe.

Derived equations of state for dark matter.

Abstract

Taking the flat rotation curve as input and treating the matter content in the galactic halo region as perfect fluid, we obtain space time metric at the galactic halo region in the framework of general relativity. We find that the resultant metric is a non-relativistic-dark-matter-induced space-time embedded in a static Friedmann-Lema\^itre-Robertson-Walker universe. This means that the flat rotation curve not only leads to the existence of dark matter but also suggests the background geometry of the universe. The flat rotation curve and the demand that the dark matter be non-exotic together indicate a (nearly) flat universe as favored by the modern cosmological observations. We obtain the expressions for energy density and pressure of dark matter halo and consequently the equation of state of dark matter. Various other aspects of the solution are also analyzed.