  Scalar-Tensor-Vector Gravity (STVG), also referred as MOdified Gravity (MOG),
is an alternative theory of the gravitational interaction. Its weak field
approximation has been successfully used to described Solar System
observations, galaxy rotation curves, dynamics of clusters of galaxies, and
cosmological data, without the imposition of dark components. The theory was
formulated by John Moffat in 2006. In this work, we derive matter-sourced
solutions of STVG and construct neutron star models. We aim at exploring STVG
predictions about stellar structure in the strong gravity regime. Specifically,
we represent spacetime with a static, spherically symmetric manifold, and model
the stellar matter content with a perfect fluid energy-momentum tensor. We then
derive the modified Tolman-Oppenheimer-Volkoff equation in STVG and integrate
it for different equations of state. We find that STVG allows heavier neutron
stars than General Relativity (GR). Maximum masses depend on a normalized
parameter that quantifies the deviation from GR. The theory exhibits unusual
predictions for extreme values of this parameter. We conclude that STVG admits
suitable spherically symmetric solutions with matter sources, relevant for
stellar structure. Since recent determinations of neutron stars masses violate
some GR predictions, STVG appears as a viable candidate for a new gravity
theory.
