Vacuum Polarization Instead of “Dark Matter” in a Galaxy

Abstract

We considered a vacuum polarization inside a galaxy in the eikonal approximation and found that two possible types of polarization exist. The first type is described by the equation of state p=ρ/3, similar to radiation. Using the conformally unimodular metric allows us to construct a non-singular solution for this vacuum “substance” if a compact astrophysical object exists in the galaxy’s center. As a result, a “dark” galactical halo appears that increases the rotation velocity of a test particle as a function of the distance from a galactic center. The second type of vacuum polarization has a more complicated equation of state. As a static physical effect, it produces the renormalization of the gravitational constant, thus, causing no static halo. However, a non-stationary polarization of the second type, resulting from an exponential increase (or decrease) of the galactic nuclei mass with time in some hypothetical time-dependent process, produces a gravitational potential, appearing similar to a dark matter halo.