Disformal transformation of physical quantities associated with relativistic stars

Understand

We investigate how physical quantities associated with relativistic stars in the Jordan and Einstein frames are related by the generalized disformal transformations constructed by the scalar and vector fields within the slow-rotation approximation.

• We consider the most general scalar disformal transformation constructed by the scalar field, and by the vector field without and with the $U(1)$ gauge symmetry, respectively.
• At the zeroth order of the slow-rotation approximation, by imposing that both the metrics of the Jordan and Einstein frames are asymptotically flat, we show that the Arnowitt-Deser-Misner mass is frame invariant.
• At the first order of the slow-rotation approximation, we discuss the disformal transformations of the frame-dragging function, angular velocity, angular momentum, and moment of inertia of the star.