Vector field and rotational curves in dark galactic halos

We study equations of a non-gauge vector field in a spherically symmetric static metric. The constant vector field with a scale arrangement of components: the time component about the Planck mass m_{Pl} and the radial component about M suppressed with respect to the Planck mass, serves as a source of metric reproducing flat rotation curves in dark halos of spiral galaxies, so that the velocity of rotation v_0 is determined by the hierarchy of scales: \sqrt{2} v_0^2= M/m_{Pl}, and M\sim 10^{12} GeV. A natural estimate of Milgrom's acceleration about the Hubble rate is obtained.

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