Dissonant Black Droplets and Black Funnels

TL;DR

This paper constructs and analyzes detuned black droplet and funnel solutions in holography, revealing the thermodynamic preference of hairy droplets over hairless ones in certain conditions.

Contribution

It introduces the first explicit construction of detuned black droplet and funnel solutions dual to a Schwarzschild background in holography.

Findings

Boulware state corresponds to a droplet solution.

Hairy black droplets are thermodynamically favored at low temperatures.

Constructed explicit detuned solutions for black funnels and droplets.

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.