The paper by Robert M. Wald explores the relationship between black hole entropy and Noether charges in a general classical theory of gravity. Wald demonstrates that for stationary black hole solutions with bifurcate Killing horizons, the first law of black hole mechanics holds for perturbations to nearby stationary black holes. The quantity playing the role of black hole entropy is defined as \(2\pi\) times the integral over the bifurcation surface \(\Sigma\) of the Noether charge associated with the horizon Killing field, normalized to have unit surface gravity. This result suggests a natural candidate for the entropy of a dynamical black hole in a general theory of gravity. Wald also shows that this black hole entropy is given by a local geometrical expression on the horizon, and that the validity of the second law of black hole mechanics is equivalent to the positivity of a total Noether flux, which is related to the positive energy properties of the theory. The paper further discusses the connection between this approach and the "Euclidean derivation" of black hole entropy, demonstrating their equivalence.The paper by Robert M. Wald explores the relationship between black hole entropy and Noether charges in a general classical theory of gravity. Wald demonstrates that for stationary black hole solutions with bifurcate Killing horizons, the first law of black hole mechanics holds for perturbations to nearby stationary black holes. The quantity playing the role of black hole entropy is defined as \(2\pi\) times the integral over the bifurcation surface \(\Sigma\) of the Noether charge associated with the horizon Killing field, normalized to have unit surface gravity. This result suggests a natural candidate for the entropy of a dynamical black hole in a general theory of gravity. Wald also shows that this black hole entropy is given by a local geometrical expression on the horizon, and that the validity of the second law of black hole mechanics is equivalent to the positivity of a total Noether flux, which is related to the positive energy properties of the theory. The paper further discusses the connection between this approach and the "Euclidean derivation" of black hole entropy, demonstrating their equivalence.