Quantum evolution of de Sitter black holes near extremality

TL;DR

This work analyzes charged, near-extremal black holes in de Sitter space, showing that, unlike in flat space, such black holes evolve toward thermal equilibrium with the cosmological horizon rather than extremality. The authors employ an effective Schwarzian theory for the near-horizon AdS$_2$ throat, coupled to the far-horizon de Sitter quantum field in the Bunch-Davies vacuum, to compute quantum energy transfer for uncharged massless scalars. They find that energy emission or absorption rates differ qualitatively from Hawking predictions: hotter BHs emit more weakly than their flat-space counterparts, while colder ones absorb energy at a nearly constant rate, due to the thermal bath of the cosmological horizon. The analysis highlights how near-horizon quantum dynamics and cosmological- horizon thermodynamics interplay to govern the evolution of de Sitter black holes and depends crucially on the vacuum choice for the far-horizon QFT.

Abstract

We study the evolution of charged, asymptotically de Sitter black holes close to the cold extremal branch of the phase space. We consider black hole sizes that are parametrically smaller than both their inverse temperature and the cosmological horizon. Unlike flat space, charged de Sitter black holes do not evolve towards extremality, but rather towards a thermal equilibrium with the cosmological horizon. In the low-temperature regime, the near-horizon physics can be effectively captured by a one-dimensional Schwarzian theory. This is coupled to the far-horizon de Sitter quantum field theory. Incorporating the thermal nature of the cosmological horizon, we compute the quantum energy transfer through uncharged massless scalar particles. The results significantly differ from Hawking's thermal predictions. Black holes that are hotter than the cosmological horizon emit energy at a rate lower than their asymptotically flat counterparts. Whereas much colder ones absorb energy at a nearly constant rate.

Figures (3)

• Figure 1: de Sitter Penrose diagram. The dashed line shows the spatial section of global de Sitter which is $\mathbb{S}^3$. The highlighted area is the static patch for an observer at south pole. The static time arrow is also shown.
• Figure 2: A Schematic diagram of electrically charged dS black hole phase space
• Figure 3: Evolution of small near-extremal black holes. Here we zoomed in near the cold branch for small black holes in phase space.