Exact Metric for a Nonrotating Mass with a Quadrupole Moment

Abstract
Erez and Rosen have given a method for calculating an exact static metric for a nonrotating, cylindrically symmetric mass distribution possessing multipole moments of arbitrary order; however, the explicit expressions they give for the metric components arising from a combination of monopole and quadrupole moments contain errors. In this paper, we sketch the Erez-Rosen method and then state the corrected form of the metric for this experimentally significant case of a mass distribution with monopole and quadrupole moments.