Noether charge form of the first law of black hole mechanics - art. no. 064009

The first law of black hole mechanics was derived by Wald in a general cova riant theory of gravity for stationary variations around a stationary black hole. It is formulated in terms of Noether charges and has many advantages . In this paper several issues are discussed to strengthen the validity of the Noether charge form of the first law. In particular, a gauge condition used in the derivation is justified. After that, we justify the generalizat ion to nonstationary variations done by Iyer and Wald. [S0556-2821(99)03004 -0].