Abstract
In a space-time with cosmological constant and matter satisfying the dominant energy condition, the area of a black or white hole cannot exceed . 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 cannot merge. We discuss the conjectured isoperimetric inequality and implications for the cosmic censorship conjecture.
- Received 30 August 1993
DOI:https://doi.org/10.1103/PhysRevD.49.5080
©1994 American Physical Society