Slowly Rotating Relativistic Stars in Scalar-Tensor Gravity

We consider the slowly rotating relativistic stars with a uniform angular velocity in the scalar-tensor gravity, and examine the rotational effect around such compact objects. For this purpose, we derive a 2nd order differential equation describing the frame dragging in the scalar-tensor gravity and solve it numerically. As a result, we find that the total angular momentum is proportional to the angular velocity even in the scalar-tensor gravity. We also show that one can observe the spontaneous scalarization in rotational effects as well as the other stellar properties, if the cosmological value of scalar field is zero. On the other hand, if the cosmological value of scalar field is nonzero, the deviation from the general relativity can be seen in a wide range of the coupling constant. Additionally, we find that the deviation from the general relativity becomes larger with more massive stellar models, which is independent of the cosmological value of scalar field. Thus, via precise observations of astronomical phenomena associated with rotating relativistic stars, one may be possible to probe not only the gravitational theory in the strong-field regime, but also the existence of scalar field.