Dragging of inertial frames inside the rotating neutron stars

Abstract

We derive the exact frame-dragging rate inside rotating neutron stars. This formula is applied to show that the frame-dragging rate monotonically decreases from the centre to the surface of the neutron star along the pole. In case of frame-dragging rate along the equatorial distance, it decreases initially away from the centre, becomes negligibly small well before the surface of the neutron star, rises again and finally approaches to a small value at the surface. The appearance of local maximum and minimum in this case is the result of the dependence of frame-dragging frequency on the distance and angle. Moving from the equator to the pole, it is observed that this local maximum and minimum in the frame dragging rate along the equator disappears after crossing a critical angle. It is also noted that the positions of local maximum and minimum of the frame-dragging rate along the equator depend on the rotation frequency and central energy density of a particular pulsar.