  The solutions for the Tolmann-Oppenheimer-Volkoff (TOV) equation bring
valuable informations about the macroscopical features of compact astrophysical
objects as neutron stars. They are sensitive to both the equation of state
considered for nuclear matter and the background gravitational theory. In this
work we construct the TOV equation for a conservative version of the $f(R,T)$
gravity. While the non-vanishing of the covariant derivative of the $f(R,T)$
energy-momentum tensor yields, in a cosmological perspective, the prediction of
creation of matter throughout the universe evolution as shown by T. Harko, in
the analysis of the hydrostatic equilibrium of compact astrophysical objects,
this property still lacks a convincing physical explanation. The imposition of
$\nabla^{\mu}T_{\mu\nu}=0$ demands a particular form for the function $h(T)$ in
$f(R,T)=R+h(T)$, which is here derived. Therefore, the choice of a specific
equation of state for the star matter demands a unique form of $h(T)$,
manifesting a strong connection between conserved $f(R,T)$ gravity and the star
matter constitution. We construct and solve the TOV equation for the general
equation of state for $p=k\rho^{\Gamma}$, with $k$ being the EoS parameter,
$\rho$ {\it the energy density} and $\Gamma$ is the adiabatic index. We also
derive the macroscopical properties of neutron stars ($\Gamma=5/3$) within this
approach.
