  Lorentz violation is motivated by quantum gravity and it is generically
described by nondynamical tensors. In this work a Lorentz violating extension
of general relativity is studied where a nondynamical tensor couples to the
Weyl tensor. A family of static and spherically symmetric solutions in vacuum
is found, confirming that there are consistent solutions with explicit Lorentz
violation in dynamical spacetimes. These solutions produce an unconventional
dependence of the gravitational redshift, which, in turn, leads to the first
bounds on such nondynamical tensor that do not rely on the physics of the early
universe. Moreover, the bounds obtained in this work are competitive with
respect to limits on similar nondynamical tensors.
