Abstract
A holographic field theory on a fixed black hole background has a gravitational dual represented by a black funnel or a black droplet. These states are ‘detuned’ when the temperature of the field theory near the horizon does not match the temperature of the background black hole. In particular, the gravitational dual to the Boulware state must be a detuned solution. We construct detuned droplets and funnels dual to a Schwarzschild background and show that the Boulware phase is represented by a droplet. We also construct hairy black droplets associated to a low-temperature scalar condensation instability and show that they are thermodynamically preferred to their hairless counterparts.
Highlights
The AdS/CFT correspondence [1,2,3] provides a powerful means of studying strongly coupled quantum field theories in curved spacetimes
A holographic field theory on a fixed black hole background has a gravitational dual represented by a black funnel or a black droplet
In the limit in which the bulk is described by classical general relativity, the gravitational duals are asymptotically locally AdS spacetimes which can roughly be divided into two classes: ‘black funnels’ and ‘black droplets’
Summary
The AdS/CFT correspondence [1,2,3] provides a powerful means of studying strongly coupled quantum field theories in curved spacetimes. If the mass of the scalar is chosen such that μ2 2 < −1/4, so that it violates the BreitenlöhnerFreedman (BF) [21] bound of the near-horizon AdS26, an instability develops causing the scalar field to condense around the horizon This hairy solution is thermodynamically preferred, and a theory containing such a bulk matter field will have a different Boulware state from one without it. To illustrate this phenomenon explicitly, we will introduce a scalar field φ and construct black droplets which are solutions to the Einstein–Klein–Gordon system.
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