  In this work, we study the influence of $f(R,T)$ gravity on rapidly rotating
neutron stars. First we discuss the main aspects of this modified theory of
gravity where the gravitational Lagrangian is an arbitrary function of the
Ricci scalar $R$ and of the trace of the energy-momentum tensor $T$. Then we
present the basic equations for neutron stars including the equations of state
used in the present work to describe the hadronic matter. Some physical
quantities of interest are calculated such as mass-radius relations, moments of
inertia, angular momentum, and compactness. By considering four different
rotation regimes, we obtain results that indicate substantial modifications in
the physical properties of neutron stars in $f(R,T)$ gravity when compared to
those in the context of general relativity. In particular, the mass-radius
relation for sequences of stars indicates that $f(R,T)$ gravity increases the
mass and the equatorial radius of the neutron stars for stars rotating with an
angular velocity smaller than Kepler limit.
