A Cosmological Constant Limits the Size of Black Holes

Details A Cosmological Constant Limits the Size of Black Holes A Cosmological Constant Limits the Size of Black Holes

1993-09-02

arxiv.org/abs/gr-qc/9309004v2

Phys.Rev. D49 (1994) 5080-5085

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages

Scientific paper

10.1103/PhysRevD.49.5080

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.

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