Linearization stability of gravitational and gauge fields

Conditions are given for the linearization stability of the Yang–Mills and the Einstein–Yang–Mills equations on a spacetime with a compact Cauchy surface. There are sufficient conditions on the Cauchy surface, and necessary and sufficient conditions on the spacetime; the latter are identified with global infinitesimal symmetries of the principal fiber bundle associated with the Yang–Mills (gauge) field. For each system a splitting theorem for the initial data is given and the Cauchy problem is discussed.