Can large black holes collide in de Sitter space-time? An inflationary scenario of an inhomogeneous universe

Abstract

We investigate black holes in asymptotically de Sitter space-times. We show that a trapped surface always appears inside the event horizon and the total area of the black holes does not decrease as in asymptotically flat space-times. We find, however, that there is an upper bound on the area of apparent horizons in a wide class of asymptotically de Sitter space-times, in contrast with asymptotically flat space-times. This implies that black holes with a large area cannot collide with each other in asymptotically de Sitter space-time, unless a naked singularity is formed. On the basis of these results we argue that the inflationary scenario works even for initially inhomogeneous universes.

Upper bound for entropy in asymptotically de Sitter space-time

“…Shiromizu, Nakao, Kodama and Maeda [5] also obtained the same conclusion on a maximal hypersurface. However, one cannot say that the same conclusion holds for CEHs in a general non-stationary asymptotically de Sitter space-time, because it is highly nontrivial whether a foliation by such hypersurfaces exists and covers the relevant portion of the space-time.…”

“…As a precise definition of an asymptotically de Sitter space-time satisfying the WCC, we assume space-time (M, g) to be strongly asymptotically predictable from a partial Cauchy surface Σ and de Sitter in the future [5], and just call it asymptotically de Sitter. In what follows, causal relationships are considered in a larger manifold (M ,g) in which (M, g) is conformally embedded.…”

“…Hayward, Shiromizu and Nakao [4] and Shiromizu, Nakao, Kodama and Maeda [5] showed that the area of a BEH in the asymptotically de Sitter space-time cannot decrease and has an upper bound 4π/Λ if the weak cosmic censorship (WCC) [6] holds. It means that black holes cannot collide each other if the total area of them exceeds the upper bound.…”

On the hologram of de Sitter

“…If the spatial slices have punctures, we will have to deal with holonomies of G. We will postpone this discussion to the next section. The on-shell condition now translates into A t = −ĠG −1 = iℓ −1 γ 0 , meaning that we can write G = e −iℓ −1 tγ0 g(z,z), with g independent of t. Changing variables in (11), and using the fact that the resulting action depends only on the boundary values of G, one arrives at:…”

“…The main advantage of this approach is to make a clear distinction between what is considered "gauge choice" in the Chern-Simons language and what is considered "on-shell". Following Shiromizu et al [11] (after similar work done for AdS by Hawking and by Ashtekhar and Magnon [12]), we will say that a ndimensional spacetime with metric g ab is asymptotically de Sitter when 1. The causal boundary of space-time is I + ∪ I − [13].…”