Derivation of the Tully-Fisher Law from General Relativity Theory: Doubts about the Existence of Halo Dark Matter

Abstract

Observations show that for disk galaxies the fourth power of the circular velocity of stars around the core of the galaxy is proportional to the luminosity L. This is known as the Tully-Fisher law. Since L is proportional to the mass M of the galaxy, it follows that the fourth power of the circular velocity is proportional to M. Newtonian mechanics, however, tells that the square of the circular velocity is proportional to M. In order to rectify this big difference, astronomers assume the existence of halo dark matter. In this paper we show that general relativity theory yields a term of the Tully-Fisher form. This puts doubts about the necessity and existence of halo dark matter for galaxies.