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 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.

中文翻译：

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真空极化而不是星系中的“暗物质”

我们在 eikonal 近似中考虑了星系内部的真空极化，并发现存在两种可能的极化类型。第一种类型由状态方程描述$p=\rho /3$，类似于辐射。如果星系中心存在一个致密的天体物理物体，使用共形单模度量允许我们为这种真空“物质”构建一个非奇异解。结果，出现了一个“暗”星系晕，它增加了测试粒子的旋转速度，作为距星系中心距离的函数。第二种真空极化具有更复杂的状态方程。作为一种静态物理效应，它会产生引力常数的重整化，因此不会产生静态光晕。然而，第二种类型的非平稳极化是由于在一些假设的时间相关过程中星系核质量随时间呈指数增加（或减少）而产生的，它会产生引力势，看起来类似于暗物质晕。