Abstract.We criticize and generalize some properties of Nöther charges presented in a paper by V. Iyer and R. M. Wald and their application to entropy of black holes. The first law of black holes thermodynamics is proven for any gauge-natural field theory. As an application charged Kerr-Newman solutions are considered. As a further example we consider a (1 + 2) black hole solution.

A general recipe to define, via Nöther theorem, the Hamiltonian in any natural field theory is suggested. It is based on a Regge-Teitelboim-like approach applied to the variation of Nöther conserved quantities. The Hamiltonian for General Relativity in presence of non-orthogonal boundaries is analysed and the energy is defined as the on-shell value of the Hamiltonian. The role played by boundary conditions in the formalism is outlined and the quasilocal internal energy is defined by imposing metric Dirichlet boundary conditions. A (conditioned) agreement with previous definitions is proved. A correspondence with Brown-York original formulation of the first principle of black hole thermodynamics is finally established.

A geometrical framework for the definition of entropy in general relativity via the No ther theorem is briefly recalled, and the entropy of Taub Bolt Euclidean solutions of Einstein equations is then obtained as an application. The computed entropy agrees with previously known results, obtained by statistical methods. It was generally believed that the entropy of a Taub Bolt solution could not be computed via the No ther theorem, due to the particular structure of the singularities of this solution. We show here that this is not true. The Misner string singularity is, in fact, considered, and its contribution to the entropy is analyzed. As a result, in our framework entropy does not obey the``one-quarter area law'' and it is not directly related to horizons, as is sometimes erroneously suggested in the current literature on the subject. Academic Press