Effects of General Relativistic Spin Precessions on the Habitability of Rogue Planets Orbiting Supermassive Black Holes

Recently, the possibility that several starless telluric planets may form around supermassive black holes (SMBHs) and receive 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 _• = 1 × 10⁸ M _⊙ 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 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, ε, to its orbital plane by tens to hundreds of degrees over a time span of, say, just Δt = 400 yr, strongly depending on the obliquity η _• 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.