  Within the framework of $f(R,T)$ theories of gravity, we investigate the
hydrostatic equilibrium of anisotropic neutron stars with a physically relevant
equation of state (EoS) for the radial pressure. In particular, we focus on the
$f(R,T) = R+ 2\beta T$ model, where $\beta$ is a minimal coupling constant. In
the slowly rotating approximation, we derive the modified TOV equations and the
expression for the relativistic moment of inertia. The main properties of
neutron stars, such as radius, mass and moment of inertia, are studied in
detail. Our results revel that the main consequence of the $2\beta T$ term is a
substantial increase in the surface radius for low enough central densities.
Nevertheless, such a term slightly modifies the total gravitational mass and
moment of inertia of the slowly rotating stars. Furthermore, the changes are
noticeable when anisotropy is incorporated into the stellar fluid, and it is
possible to obtain higher masses that are consistent with the current
observational data.

General Relativity and Quantum Cosmology