Linear Potentials and Galactic Rotation Curves - Formalism

Abstract

In the first paper in this series we presented a typical set of galactic rotation curves associated with the conformal invariant fourth order theory of gravity which has recently been advanced by Mannheim and Kazanas as a candidate alternative to the standard second order Einstein theory. Reasonable agreement with data was obtained for four representative galaxies without the need for any non-luminous or dark matter. In this second paper we present the associated formalism. Additionally, we discuss the status of the Tully-Fisher relation in our theory, compare and contrast our theory with the dark matter theory, and make some general observations regarding the systematics of galactic rotation curve data.