Scalar-tensor theories are one of the most well-known alternative to General Relativity. They violate the Strong Equivalence Principle: this is parametrized by the so-called sensitivities, which encode how the mass of an astrophysical object depends on the scalar field. Sensitivities enter in many observable quantities in scalar-tensor theories, including waveforms of binary neutron stars or trajectories of binary pulsars. In this talk, I will present a new kind of sensitivity related to changes of the moment of inertia of neutron stars induced by the scalar field. I will clarify subtle issues about conservation laws in the Jordan or Einstein frame, and I will show how one can numerically compute these angular momentum sensitivities. Finally, I will present an application to constrain the couplings of ultra-light dark matter models
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