Cosmological N-body simulations on structure formation in a Λ−CDM scenario point to a mass
density distribution of dark matter, in local objects like galaxies, that are in strong tension with
recent observations on low surface brightness galaxies. Modified theories of gravity lack of this
problem but also find tensions with observations at larger scales. In this thesis we study the
main methods for galaxy rotation curve fitting, from modified theories of gravity such as MOND
and f (R) = R n , and considering dark matter halos, such as the one derived from the Λ−CDM
numerical simulations and the phenomenological Burkert cored halo profile. To investigate the
properties of the dark matter halo that surrounds galaxies, two methods are examined: the
standard mass modeling and the local density method. All these methods are applied to the
study of the rotation curve of the galaxy M33, which is well extended and measured with an
unprecedent high spatial resolution. Later on, we present a unified parameterization of the
circular velocity which accurately fits 887 galactic rotation curves without needing in advance
the knowledge of the luminous matter components, nor a fixed dark matter halo model. A
notable feature of this parametrization is that the associated gravitational potential increases
with the distance from the galactic center, giving rise to a length scale indicating a finite size
of a galaxy, and after, the keplerian fall-off of the velocity is recovered, making possible for the
prediction of the total mass enclosed by the galaxy. As the keplerian regime is reached after
a finite length scale, based on isotropy and homogeneity arguments, we considered a static
and spherically symmetric Schwarzschild-like space time embedding each galaxy, such that any
massive particle moving in geodesic circumferences in the equatorial plane, turns around origin
of coordinates with the newly found parameterized velocity formula. Appealing to the General
Relativity field equations, for a perfect fluid with pressure anisotropies, we found that the dark
matter halo behaves like a cosmological constant in the outer parts of galaxies and controls the
distribution shape of the luminous matter component by means of the anisotropic pressure in
the azimuthal direction.
