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 4π/Λ. This applies to event horizons where defined, i.e. in an asymptotically deSitter 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 ‘SchwarzschilddeSitter’ solution. This yields a topological restriction on the event horizon, namely that components whose total area exceeds 4π/Λ cannot merge. We discuss the conjectured isoperimetric inequality and implications for the cosmic censorship conjecture.