  Scalar-tensor theories have a long history as possible phenomenological
alternatives to General Relativity, but are known to potentially produce
deviations from the (strong) equivalence principle in systems involving
self-gravitating objects, as a result of the presence of an additional
gravitational scalar field besides the tensor modes of General Relativity. We
describe here a novel mechanism whereby the equivalence principle is violated
for an isolated rotating neutron star, if the gravitational scalar field is
changing in time far from the system. We show that the neutron star rotational
period changes due to an effective coupling ("angular momentum sensitivity") to
the gravitational scalar, and compute that coupling for viable equations of
state for nuclear matter. We comment on the relevance of our findings for
testing scalar-tensor theories and models of ultralight dark matter with pulsar
timing observations, a topic that we tackle in a companion paper.
