II. A GR Source Term $T^{\mu \nu}$ For Dark Matter

TL;DR

This paper proposes new models for dark matter's energy-momentum tensor, explaining galaxy rotation curves and suggesting that dark energy may be an artifact of incorrect assumptions about dark matter's properties.

Contribution

It introduces two forms of the dark matter energy-momentum tensor, linking pressure effects to galaxy rotation curves and cosmological implications, challenging conventional dark energy interpretations.

Findings

Galaxy rotation curves can be explained by pressure-dominated dark matter models.

Dark matter cannot approach closer than ~4 kpc to galactic centers.

Some dark energy effects may result from improper dark matter equations of state.

Abstract

Two forms are suggested for the energy-momentum source term associated with an aggregate of dark matter (with the properties described in Paper I). Both have large pressure-like components which dominate the density terms. Using one form a simple model of the spiral galaxy halos is developed which can match the observed `flat' outer rotation curves of some galaxies,including the Milky Way. It can also represent the ascending outer rotational curves of small spiral galaxies such as M33. See Figs. 1, 2. The halo dark matter (DM)`missing mass' results from ignoring the pressure term's contribution to the source tensor. The analysis of the Milky Way rotation curve gives parameters characterizing the DM intergalactic medium in which the halo is situated.. The dark matter cannot come closer to the galactic center than $R \sim 4$ kpc. It reaches a maximum flux at $R_h \simeq 8$ kpc and then falls rapidly with distance. It is hoped that by analyzing other galactic rotation curves these models can be used to infer properties of the intergalactic DM matter. The other form for $T^{\mu \nu}$ for DM is useful in cosmology. Then a (non-constant) cosmological `constant' term $\Lambda$ needs to be added to Einstein's equation in order to allow use for DM of the standard equation of state relation of ordinary matter.. We suggest that at least some of the `dark energy' present results from this requirement and may not be real; it simply results from adopting an improper equation of state for DM.