A Cosmological Constant Limits the Size of Black Holes

TL;DR

This paper establishes an upper limit on the size of black holes in de Sitter space, linking the cosmological constant to horizon area and implications for horizon topology and cosmic censorship.

Contribution

It proves a universal area bound for black and white holes in spacetimes with positive cosmological constant, connecting horizon size to the cosmological constant and horizon topology.

Findings

Black hole horizon area cannot exceed 4π/Λ in de Sitter space.

The bound is achieved only by the Schwarzschild-de Sitter solution.

Horizon components larger than this cannot merge, restricting topology.

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.