A Cosmological Constant Limits the Size of Black Holes

Abstract

In a space-time with cosmological constant $\Lambda >0$ and matter satisfying the dominant energy condition, the area of a black or white hole cannot exceed $4\pi /\Lambda$. 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 $4\pi /\Lambda$ cannot merge. We discuss the conjectured isoperimetric inequality and implications for the cosmic censorship conjecture.

10 pages

References in corpus (5)

• General Laws of Black-Hole Dynamics
• Quasi-Local Gravitational Energy
• Cosmological Multi-Black Hole Solutions
• Testing Cosmic Censorship with Black Hole Collisions
• Global Structure of a Black-Hole Cosmos and its Extremes

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