Enlarged Transformation Group: Star Models,Dark Matter Halos and Solar System Dynamics

TL;DR

This paper extends a geometric theory of spacetime with an enlarged transformation group, developing solutions that could explain dark matter, the Pioneer anomaly, and solar corona heating.

Contribution

It introduces a new geometric framework based on the conservation group, extending previous theories with a source-inclusive Lagrangian and solutions relevant to astrophysical phenomena.

Findings

External stress-energy tensor has non-compact support.

Models align with Schwarzschild solutions internally and externally.

Potential explanations for dark matter and Pioneer anomaly.

Abstract

Previously a theory has been presented which extends the geometrical structure of a real four-dimensional space-time via a field of orthonormal tetrads with an enlarged transformation group. This new transformation group, called the conservation group, contains the group of diffeomorphisms as a proper subgroup and we hypothesize that it is the foundational group for quantum geometry. The fundamental geometric object of the new geometry is the curvature vector, C^\mu . Using the scalar Lagrangian density C^\mu C_\mu \sqrt{-g}, field equations for the free field have been obtained which are invariant under the conservation group. In this paper, this theory is further extended by development of a suitable Lagrangian for a field with sources. Spherically symmetric solutions for both the free field and the field with sources are given. A stellar model and an external, free-field model are developed. The theory implies that the external stress-energy tensor has non-compact support and hence may give the geometrical foundation for dark matter. The resulting models are compared to the internal and external Schwarzschild models. The theory may explain the Pioneer anomaly and the corona heating problem.