Dark Matter and Non-Newtonian Gravity From General Relativity on a Stringy Background

Abstract

An exact solution of Einstein's field equations for a static spherically symmetric medium with a radially boost invariant energy-momentum tensor is presented. In the limit of an equation of state corresponding to a distribution of radially directed strings there is a $1/r$ correction to Newton's force law. At large distances and small accelerations this law coincides with the phenomenological force law invented by Milgrom in order to explain the flat rotation curves of galaxies without introducing dark matter. The present model explaines why the critical acceleration of Milgrom is of the same order of magnitude as the Hubble parameter.