GENERAL LAWS OF BLACK-HOLE DYNAMICS

A general definition of a black hole is given, and general''laws of bl ack-hole dynamics'' derived. The definition involves something similar to an apparent horizon, a trapping horizon, defined as a hypersurface foliated by marginal surfaces of one of four nondegenerate types, des cribed as future or past, and outer or inner. If the boundary of an in extendible trapped region is suitably regular, then it is a (possibly degenerate) trapping horizon. The future outer trapping horizon provid es the definition of a black hole. Outer marginal surfaces have spheri cal or planar topology. Trapping horizons are null only in the instant aneously stationary case, and otherwise outer trapping horizons are sp atial and inner trapping horizons are Lorentzian. Future outer trappin g horizons have nondecreasing area form, constant only in the null cas e: the ''second law.'' A definition of the trapping gravity of an oute r trapping horizon is given, generalizing surface gravity. The total t rapping gravity of a compact outer marginal surface has an upper bound , attained if and only if the trapping gravity is constant: the ''zero th law.'' The variation of the area form along an outer trapping horiz on is determined by the trapping gravity and an energy flux: the ''fir st law.''