  Ground states are a well-known class of Hadamard states in smooth spacetimes.
In this paper we show that the ground state of the Klein-Gordon field in a
non-smooth ultrastatic spacetime is an adiabatic state. The order of the state
depends linearly on the regularity of the metric. We obtain the result by
combining microlocal estimates for the causal propagator, propagation of
singularities results for non-smooth pseudodifferential operators, and
eigenvalue asymptotics for elliptic operators of low regularity.
