Abstract
We present a closed-form solution to Kerr black hole in the harmonic coordinate system. The formulation reduces to the post-Newtonian (PN) approximation for the rotating spherically symmetric system in the far-field limit. Basing on the harmonic metric, we also derive the analytical formulations for the 2PN dynamics of particle and photon for Kerr black hole. The harmonic form of Kerr metric in the horizon-penetrating coordinates is also presented.
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