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Previously a theory has been presented which extends the geometricalstructure of a real four-dimensional space-time via a field of orthonormaltetrads with an enlarged transformation group. This new transformation group,called the conservation group, contains the group of diffeomorphisms as aproper subgroup and we hypothesize that it is the foundational group forquantum geometry. The fundamental geometric object of the new geometry is thecurvature vector, C^\mu . Using the scalar Lagrangian density C^\mu C_\mu\sqrt{-g}, field equations for the free field have been obtained which areinvariant under the conservation group. In this paper, this theory is furtherextended by development of a suitable Lagrangian for a field with sources.Spherically symmetric solutions for both the free field and the field withsources are given. A stellar model and an external, free-field model aredeveloped. The theory implies that the external stress-energy tensor hasnon-compact support and hence may give the geometrical foundation for darkmatter. The resulting models are compared to the internal and externalSchwarzschild models. The theory may explain the Pioneer anomaly and the coronaheating problem.

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