Classification of Surface Charges for a spin two field on a curved Background solution

Within the framework of local BRST cohomology, we establish that nontrivial conserved n- 2 forms for a spin 2 field on a background corresponding to a solution to Einstein's equation with or without cosmological constant are characterized uniquely by the Killing vector fields of the background. This result is crucial in various applications in gravitation, in particular for the study of consistent interactions of spin 2 fields on curved backgrounds. It provides a nontrivial generalization of an analogous result proved in the flat case.