Einstein-Yang-Mills Theory: Gauge Invariant Charges and Linearization Instability

Understand

We construct the gauge-invariant electric and magnetic charges in Yang-Mills theory coupled to cosmological General Relativity (or any other geometric gravity), extending the flat spacetime construction of Abbott and Deser.

• For non-vanishing background gauge fields, the charges receive non-trivial contribution from the gravity part.
• In addition, we study the constraints on the first order perturbation theory and establish the conditions for linearization instability: that is the validity of the first order perturbation theory.