Upper bound for entropy in asymptotically de Sitter space-time

TL;DR

This paper establishes an upper bound on the combined entropy of black holes and cosmological horizons in asymptotically de Sitter space-times, assuming dominant energy condition and cosmic censorship.

Contribution

It derives a new upper bound for the total horizon area and entropy in de Sitter space-times with black holes, extending understanding of horizon thermodynamics.

Findings

Total horizon area is less than 12π/Λ.

Second law of horizon area holds under specified conditions.

Total entropy is bounded above by a function of the cosmological constant.

Abstract

We investigate nature of asymptotically de Sitter space-times containing a black hole. We show that if the matter fields satisfy the dominant energy condition and the cosmic censorship holds in the considering space-time, the area of the cosmological event horizon for an observer approaching a future timelike infinity does not decrease, i.e. the second law is satisfied. We also show under the same conditions that the total area of the black hole and the cosmological event horizon, a quarter of which is the total Bekenstein-Hawking entropy, is less than $12\pi/\Lambda$, where $\Lambda$ is a cosmological constant. Physical implications are also discussed.