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Relativistic stars in scalar-tensor theories with disformal coupling

We present a general formulation to analyze the structure of slowly rotating relativistic stars in a broad class of scalar-tensor theories with disformal coupling to matter. Our approach includes theories with generalized kinetic terms, generic scalar field potentials and contains theories with conformal coupling as particular limits. In order to investigate how the disformal coupling affects the structure of relativistic stars, we propose a minimal model of a massless scalar-tensor theory and investigate in detail how the disformal coupling affects the spontaneous scalarization of slowly rotating neutron stars. We show that for negative values of the disformal coupling parameter between the scalar field and matter, scalarization can be suppressed, while for large positive values of the disformal coupling parameter stellar models cannot be obtained. This allows us to put a mild upper bound on this parameter. We also show that these properties can be qualitatively understood by linearizing the scalar field equation of motion in the background of a general-relativistic incompressible star. To address the intrinsic degeneracy between uncertainties in the equation-of-state of neutron stars and gravitational theory, we also show the existence of universal equation-of-state-independent relations between the moment of inertia and compactness of neutron stars in this theory. We show that in a certain range of the theory's parameter space the universal relation largely deviates from that of general relativity, allowing, in principle, to probe the existence of spontaneous scalarization with future observations.