Black holes in dS$_3$

Abstract

In three-dimensional de Sitter space classical black holes do not exist, and the Schwarzschild-de Sitter solution instead describes a conical defect with a single cosmological horizon. We argue that the quantum backreaction of conformal fields can generate a black hole horizon, leading to a three-dimensional quantum de Sitter black hole. Its size can be as large as the cosmological horizon in a Nariai-type limit. We show explicitly how these solutions arise using braneworld holography, but also compare to a non-holographic, perturbative analysis of backreaction due to conformally coupled scalar fields in conical de Sitter space. We analyze the thermodynamics of this quantum black hole, revealing it behaves similarly to its classical four-dimensional counterpart, where the generalized entropy replaces the classical Bekenstein-Hawking entropy. We compute entropy deficits due to nucleating the three-dimensional black hole and revisit arguments for a possible matrix model description of dS spacetimes. Finally, we comment on the holographic dual description for dS spacetimes as seen from the braneworld perspective.

Quasi-local energy and microcanonical entropy in two-dimensional nearly de Sitter gravity

“…Including semi-classical backreaction, the first law of horizon thermodynamics was modified such that the classical entropy is replaced by the generalized entropy. This is expected to be a feature for systems which include backreaction; indeed, the same modification appears in the three-dimensional semi-classical Schwarzschild-de Sitter black hole [93]. Further, in the microcanonical ensemble we found that the generalized entropy is equal to the microcanonical entropy, whose stationarity condition implies extremizing the generalized entropy, similar to recent results for eternal AdS 2 black holes [30].…”

Einstein-Maxwell theory and the Weyl double copy

“…It would also be interesting to adapt our formalism to three-dimensional spacetimes, such as the BTZ black hole [58], its quantum and de Sitter generalizations [59,60], or generalized threedimensional solutions described in [61,62]. To this end, it would be worthwhile to also attempt to extend the Cotton double copy [63] to include external sources.…”