  We study the orbital and epicyclic frequencies of particles orbiting around
rapidly rotating neutron stars and strange stars in a particular scalar-tensor
theory of gravity. We find very large deviations of these frequencies, when
compared to their corresponding values in general relativity, for the
maximum-mass rotating models. In contrast, for models rotating with spin
frequency of 700Hz (approximately the largest known rotation rate of neutron
stars), the deviations are generally small. Nevertheless, for a very stiff
equation of state and a high mass the deviation of one of the epicyclic
frequencies from its GR value is appreciable even at a spin frequency of 700Hz.
In principle, such a deviation could become important in models of
quasi-periodic oscillations in low-mass x-ray binaries and could serve as a
test of strong gravity (if other parameters are well constraint). Even though
the present paper is concentrated mainly on orbital and epicyclic frequencies,
we present here for the first time rapidly rotating, scalarized equilibrium
compact stars with realistic hadronic equations of state and strange matter
equation of state. We also provide analytical expressions for the exterior
spacetime of scalarized neutron stars and their epicyclic frequencies in the
nonrotating limit.
