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 (Formula presented.), 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