Physical Review D, vol.103, no.8, 2021 (SCI-Expanded)
© 2021 American Physical Society.We construct analytical initial data for a slowly moving and rotating black hole for generic orientations of the linear momentum and the spin. We solve the Hamiltonian constraint approximately and work out the properties of the apparent horizon and show the dependence of its shape on the angle between the spin and the linear momentum. In particular, a dimple, whose location depends on the mentioned angle, arises on the two-sphere geometry of the apparent horizon. We exclusively work in the case of conformally flat initial metrics.