By focusing on the mostly used variational methods, this monograph aspires
to give a unified description and comparison of various ways of
constructing conserved quantities for perturbations and to study
symmetries in general relativity and modified theories of gravity. The
main emphasis lies on the field-theoretical covariant formulation of
perturbations, the canonical Noether approach and the Belinfante procedure
of symmetrisation. The general formalism is applied to build the
gauge-invariant cosmological perturbation theory, conserved currents and
superpotentials to describe physically important solutions of gravity
theories. Meticulous attention is given to the construction of conserved
quantities in asymptotically-flat spacetimes as well as in asymptotically
constant curvature spacetimes such as the Anti-de Sitter space.
Significant part of the book can be used in graduate courses on
conservation laws in general relativity.