Nonlinear Perturbations and Conservation Laws on Curved Backgrounds in GR and Other Metric Theories

Understand

The field-theoretical approach is reviewed.

• Perturbations in general relativity as well as in an arbitrary $D$-dimensional metric theory are studied on a background, which is a solution (arbitrary) of the theory.
• Lagrangian for perturbations is defined, and field equations for perturbations are derived from the variational principle.
• These equations are exact and equivalent to the equations in the standard formulation, but can be approximate also.