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3EEB4400-CDBB-4D50-9DC8-E19C5FCDF233

# Vacuum polarization instead of "dark matter" in a galaxy

Sergey L. Cherkas and Vladimir L. Kalashnikov

Submitted on 1 September 2022

## 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 $p=\rho /3$, similar to radiation. Using the conformally-unimodular metric allows constructing a nonsingular 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 renormalization of the gravitational constant, thus, causing no static halo. However, a nonstationary 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 looking like a dark matter halo.

## Preprint

Comment: 16 pages, 6 figures

Subjects: General Relativity and Quantum Cosmology; Astrophysics - Astrophysics of Galaxies