Robert M. Wald of the University of Chicago presents a derivation of black hole entropy as a Noether charge in general theories of gravity. The paper shows that the first law of black hole mechanics holds for perturbations of stationary black holes, with the black hole entropy being $ 2\pi $ times the integral of the Noether charge associated with the horizon Killing field, normalized to have unit surface gravity. This entropy is shown to be a local, geometrical quantity on the horizon. The derivation is valid in any theory of gravity derived from a diffeomorphism-invariant Lagrangian, and it connects the second law of black hole mechanics to the positivity of a total Noether flux, suggesting a relationship with the positive energy properties of the theory. The paper also explains the relationship between this derivation and the Euclidean method for calculating black hole entropy, showing that both approaches yield the same result. The results provide a natural candidate for the entropy of a dynamical black hole in a general theory of gravity. The paper also discusses the implications of these results for the validity of the second law of black hole mechanics in general theories of gravity.Robert M. Wald of the University of Chicago presents a derivation of black hole entropy as a Noether charge in general theories of gravity. The paper shows that the first law of black hole mechanics holds for perturbations of stationary black holes, with the black hole entropy being $ 2\pi $ times the integral of the Noether charge associated with the horizon Killing field, normalized to have unit surface gravity. This entropy is shown to be a local, geometrical quantity on the horizon. The derivation is valid in any theory of gravity derived from a diffeomorphism-invariant Lagrangian, and it connects the second law of black hole mechanics to the positivity of a total Noether flux, suggesting a relationship with the positive energy properties of the theory. The paper also explains the relationship between this derivation and the Euclidean method for calculating black hole entropy, showing that both approaches yield the same result. The results provide a natural candidate for the entropy of a dynamical black hole in a general theory of gravity. The paper also discusses the implications of these results for the validity of the second law of black hole mechanics in general theories of gravity.