  Recently, it has been shown that rocky planets orbiting neutron stars can be
habitable under non unrealistic circumstances. If a distant, pointlike source
of visible light such as a Sun-like main sequence star or the gravitationally
lensed accretion disk of a supermassive black hole is present as well, possible
temporal variations $\Delta\varepsilon_\mathrm{p}(t)$ of the planet's axial
tilt $\varepsilon_\mathrm{p}$ to the ecliptic plane should be included in the
overall habitability budget since the obliquity determines the insolation at a
given latitude on a body' s surface. I point out that, for rather generic
initial spin-orbit initial configurations, general relativistic and classical
spin variations induced by the post-Newtonian de Sitter and Lense-Thirring
components of the field of the host neutron star and by its pull to the
planetary oblateness $J_2^\mathrm{p}$ may induce huge and very fast variations
of $\varepsilon_\mathrm{p}$ which would likely have an impact on the
habitability of such worlds. In particular, for a planet's distance of, say,
$0.005\,\mathrm{au}$ from a $1.4\,M_\odot$ neutron star corresponding to an
orbital period $P_\mathrm{b}=0.109\,\mathrm{d}$, obliquity shifts
$\Delta\varepsilon_\mathrm{p}$ as large as
$\varepsilon^\mathrm{max}_\mathrm{p}-\varepsilon_\mathrm{p}^\mathrm{min}\simeq
50^\circ-100^\circ$ over characteristic timescales as short as $10\,\mathrm{d}$
($J_2^\mathrm{p}$) to $3\,\mathrm{Myr}$ (Lense-Thirring) may occur for
arbitrary orientations of the orbital and spin angular momenta
$\boldsymbol{L},\,{\boldsymbol{S}}_\mathrm{ns},\,{\boldsymbol{S}}_\mathrm{p}$
of the planet-neutron star system. In view of this feature of their spins, I
dub such hypothetical planets as ``nethotrons".
