  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. We show that the angular velocity of the star is frame
invariant in all the cases. While the angular momentum and moment of inertia
are invariant under the scalar disformal transformation, they are not under the
vector disformal transformation without and with the $U(1)$ gauge symmetry.

General Relativity and Quantum Cosmology