Angular momentum sensitivities in scalar-tensor theories

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.