A framework for creating galaxy models in the geometry of the conservation group with dark matter halos and flat rotation curves

Abstract

Pandres has developed a theory which extends the geometrical structure of a real four-dimensional space-time via a field of orthonormal tetrads with an enlarged covariance group. This new group, called the conservation group, contains the group of diffeomorphisms as a proper subgroup. The free-field Lagrangian density involves only the curvature vector which is a vector which measures curvature. When massive objects are present a source term is added to this Lagrangian density. The weak-field approximation implies that gravitational waves travel at the speed of light. Spherically symmetric solutions for both the free field and the field with sources are found. In the free-field case, the field equations require nonzero stress-energy tensors. However, we find that for our model to be an acceptable model, we must have a source term in the Lagrangian. In our framework, we divide up the galaxy into three spherically symmetric regions: a baryonic matter-dominated central bulge, a dark matter-dominated mesosphere and an outside region where neither type dominates. Assuming the density of baryonic matter has a central cusp, we show how to model the bulge. Via an isothermal condition we find a model for the mesosphere and show this model implies flat rotation curves with one free parameter. The outside region is readily modeled via previously published results. The models for the bulge, mesosphere and outside region are combined into one continuous model. Using the radial acceleration relation we then show how a galaxy model may be set up for a rotationally supported galaxy.

11 pages, 1 figure

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