A Cosmological Constant Limits the Size of Black Holes

In a space-time with cosmological constant $\mathrm{\Lambda }>0$ and matter satisfying the dominant energy condition, the area of a black or white hole cannot exceed $4\pi \mathrm{/}\mathrm{\Lambda }$. 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 `Schwarzschild-deSitter’ solution. This yields a topological restriction on the event horizon, namely that components whose total area exceeds $4\pi \mathrm{/}\mathrm{\Lambda }$ cannot merge. We discuss the conjectured isoperimetric inequality and implications for the cosmic censorship conjecture.