On Dark Matter As A Geometric Effect in the Galactic Halo

We obtain more straightforwardly some features of dark matter distribution in the halos of galaxies by considering the spherically symmetric space-time, which satisfies the flat rotational curve condition, and the geometric equation of state resulting from the modified gravity theory. In order to measure the equation of state for dark matter in the galactic halo, we provide a general formalism taking into account the modified $f(X)$ gravity theories. Here, $f(X)$ is a general function of $X \in \{ R, \mathcal{G}, T \}$, where $R, \mathcal{G}$ and $T$ are the Ricci scalar, the Gauss-Bonnet scalar and the torsion scalar, respectively. These theories yield that the flat rotation curves appear as a consequence of the additional geometric structure accommodated by those of modified gravity theories. Constructing a geometric equation of state $w_{_X} \equiv p_{_X} / \rho_{_X}$ and inspiring by some values of the equation of state for the ordinary matter, we infer some properties of dark matter in galactic halos of galaxies.