Galactic Dark Matter in the Phantom Field

We investigate the possibility that the galactic dark matter exists in an scenario where the phantom field is responsible for the dark energy. We obtain the statically and spherically approximate solution for this kind of the galaxy system with a supermassive black hole at its center. The solution of the metric functions is satisfied with $g_{tt} = - g_{rr}^{-1}$. Constrained by the observation of the rotational stars moving in circular orbits with nearly constant tangential speed in a spiral galaxy, the background of the phantom field which is spatially inhomogeneous has an exponential potential. To avoid the well-known quantum instability of the vacuum at high frequencies, the phantom field defined in an effective theory is valid only at low energies. Under this assumption, we further investigate the following properties. The absorption cross section of the low-energy $S$-wave excitations of the phantom field into the central black hole is shown to be the horizontal area of the central black hole. Because the infalling phantom particles have a total negative energy, the accretion of the phantom energy is related to the decrease of the black hole mass which is estimated to be much less than a solar mass in the lifetime of the Universe. Using a simple model with the cold dark matter very weakly coupled to the "{\it low-frequency}" phantom particles which are generated from the background, we show that these two densities can be quasi-stable in the galaxy.