Precession, nutation, and variation of UT1 due to the Sun's post-Newtonian torque

We derived the post-Newtonian transformation laws of the coordinate velocity and the coordinate acceleration between a global and a body-centric coordinate system, which is related to each other by a kinematically non-rotating coordinate transformation. Next, by using the latter transformation, we obtained an explicit expression of the post-Newtonian tidal acceleration. Then, by conducting a special volume integral of torque element on an equal body-centric coordinate time hypersurface, we computed the post-Newtonian form of the gravitational torque. Finally, by integrating the Poisson approximation of the post-Newtonian extension of the Eulerian equation of rotational motion of the Earth moving along an elliptic orbit around the Sun and suffering the Sun's torque only, we evaluated post-Newtonian corrections to the precession, the nutation, and the variation of UT1. Except the geodesic precession and the geodesic nutation (Fukushima 1991), the largest effects are those related to the rotation angle of the Earth, UT1, as much as ΔUT1 = 10.50 sin l' + 0.09 sin 2l' where the unit is millisecond and l' denotes the mean anomaly of the Sun. The associated variation of the angular velocity of the Earth rotation becomes ΔΩ = 2.4 cos l' in the unit of 10^-14rad/s. These are comparable with the tidal effects due to the nonrigidity of the Earth.