  Recently, the possibility that several starless telluric planets may form
around supermassive black holes (SMBHs) and receive an energy input from the
hole's accretion disk, which, under certain plausible circumstances, may make
them habitable in a terrestrial sense, has gained increasing attention. In
particular, an observer on a planet orbiting at distance $r=100$ Schwarzschild
radii from a maximally rotating Kerr SMBH with mass $M_\bullet = 1\times
10^8\,M_\odot$ in a plane slightly outside the equator of the latter, would see
the gravitationally lensed accretion disk the same size as the Sun as seen from
the Earth. Moreover, the accretion rate might be imagined to be set in such a
way that the apparent disk's temperature would be identical to that of the
solar surface. We demonstrate that the post-Newtonian (pN) de Sitter and
Lense--Thirring precessions of the spin axis of such a world would rapidly
change, among other things, its tilt, $\varepsilon$, to its orbital plane by
tens to hundreds of degrees over a time span of, say, just $\Delta t
=400\,\mathrm{yr}$, strongly depending on the obliquity $\eta_\bullet$ of the
SMBH's spin to the orbital plane. Thus, such relativistic features would have
per se a relevant impact on the long-term habitability of the considered
planet. Other scenarios are examined as well.
