Quasi-local first law of black-hole dynamics

A property well known as the first law of black holes is a relation among i nfinitesimal variations of parameters of stationary black holes. We conside r a dynamical version of the first law, which may be called the first law o f black hole dynamics. The first law of black hole dynamics is derived with out assuming any symmetry or any asymptotic conditions. In the derivation, a definition of dynamical surface gravity is proposed. In spherical symmetr y it reduces to that defined recently by one of the authors (SAH).