Slowly Rotating Relativistic Stars in Tensor-Vector-Scalar Theory

In order to examine the rotational effect around neutron star in tensor-vector-scalar (TeVeS) theory, we consider the slowly rotating relativistic stars with a uniform angular velocity. As a result, we find that similar to the case in general relativity (GR), the angular momentum is proportional to the angular velocity. Additionally, as the value of coupling constant $K$ becomes higher, the frame dragging in TeVeS becomes quite different distribution from that in GR, where we can also see the deviation even in the interior of star. While with smaller value of $K$, although the frame dragging approaches to that expected in GR, the induced vector field due to the rotation does not vanish and still exists. Thus, through the observations associated with relativistic object, one could be possible to distinguish the gravitational theory in strong field regime even in the case that the value of coupling constant $K$ is quite small.

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