A COSMOLOGICAL CONSTANT LIMITS THE SIZE OF BLACK-HOLES

In a space-time with cosmological constant LAMBDA > 0 and matter satis fying the dominant energy condition, the area of a black or white hole cannot exceed 4pi/LAMBDA. This applies to event horizons where define d, i.e., in an asymptotically de Sitter space-time, and to outer trapp ing horizons (cf. apparent horizons) in any space-time. The bound is a ttained if and only if the horizon is identical to that of the degener ate '' Schwarzschild-de Sitter'' solution. This yields a topological r estriction on the event horizon, namely that components whose total ar ea exceeds 4pi/LAMBDA cannot merge. We discuss the conjectured isoperi metric inequality and implications for the cosmic censorship conjectur e.