  We prove boundary controllability results for wave equations (with
lower-order terms) on Lorentzian manifolds with time-dependent geometry
satisfying suitable curvature bounds. The main ingredient is a novel global
Carleman estimate on Lorentzian manifolds that is supported in the exterior of
a null (or characteristic) cone, which leads to both an observability
inequality and bounds for the corresponding constant. The Carleman estimate
also yields a unique continuation result on the null cone exterior, which has
applications toward inverse problems for linear waves on Lorentzian
backgrounds.
