  In Lorentz violating theories of gravitation with a preferred foliation a
notion of black hole is still possible, despite the presence of infinitely fast
propagating modes. Such event horizons are known as universal horizons. Their
discovery poses the question of whether they satisfy mechanical laws, analogous
to the ones of Killing horizons in Lorentz symmetric theories, and whether they
admit a thermodynamical interpretation. In this paper we study the viability of
the first law for several exact universal horizon solutions previously derived
in the literature. Our results show that a simple mechanical and
thermodynamical interpretation is problematic in these cases, and call for a
more systematic study of rotating universal horizons.
