ИСТИНА

The talk presents a review of the canonical approach developed by Joseph Katz with coauthors and a review of the field-theoretical approach developed by the author. Both of these methods present perturbations on a given (arbitrary curved) background, perturbations are finite (exact, not infinitesimal). Conserved quantities (local and integral) for such perturbations are constructed by both the methods. There are principal differences between both the approaches. What has been presented by Joseph Katz and the author in collaboration is a combination of these approaches by a generalization of the Belinfante procedure. It turns out that in general relativity the Belinfante corrected and the field-theoretical conserved quantities are coincide exactly, whereas in modifications of general relativity (like Lovelock theory) it is not so. Applications of all the aforementioned methods for description of some exact solutions, both in general relativity and in the Einstein-Gauss-Bonnet gravity, is given.