A cosmological constant limits the size of black holes

In a space-time with cosmological constant Λ>0 and matter satisfying the dominant energy condition, the area of a black or white hole cannot exceed 4πΛ. This applies to event horizons where defined, i.e., in an asymptotically de Sitter space-time, and to outer trapping horizons (cf. apparent horizons) in any space-time. The bound is attained if and only if the horizon is identical to that of the degenerate "Schwarzschild-de Sitter" solution. This yields a topological restriction on the event horizon, namely that components whose total area exceeds 4πΛ cannot merge. We discuss the conjectured isoperimetric inequality and implications for the cosmic censorship conjecture.