Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Analogue black hole merger in a polariton condensate

D. D. Solnyshkov, V. Paquelier, C. Balmisse, G. Malpuech

Abstract

Analogue studies represent an important tool in modern Physics. In particular, analogue gravity had a strong success in the recent years with the demonstrations of Hawking radiation and superradiance of analogue black holes in classical and quantum fluids. So far, the metric of the analogue black holes was mostly fixed by the conditions of the experiment, preventing the simulation of any significant evolution of their properties, such as the change of their mass, their spatial motion, gravitation attraction to other bodies, and, ultimately, black hole mergers. Polariton condensates represent a perfect setting for the analogue simulation of black hole evolution and mergers because of the velocity-dependent losses creating a convergent flow associated with each quantum vortex, which thus becomes an analogue black hole capable of spatial motion. We show that while two vortices are unable to form a common horizon, four or more vortices can exhibit a complete black hole merger, with the radius of the common horizon given by a simple geometrical law. We also discuss the difference between the horizon and the apparent horizon in these analogue black holes with quantized constituents.

Analogue black hole merger in a polariton condensate

Abstract

Analogue studies represent an important tool in modern Physics. In particular, analogue gravity had a strong success in the recent years with the demonstrations of Hawking radiation and superradiance of analogue black holes in classical and quantum fluids. So far, the metric of the analogue black holes was mostly fixed by the conditions of the experiment, preventing the simulation of any significant evolution of their properties, such as the change of their mass, their spatial motion, gravitation attraction to other bodies, and, ultimately, black hole mergers. Polariton condensates represent a perfect setting for the analogue simulation of black hole evolution and mergers because of the velocity-dependent losses creating a convergent flow associated with each quantum vortex, which thus becomes an analogue black hole capable of spatial motion. We show that while two vortices are unable to form a common horizon, four or more vortices can exhibit a complete black hole merger, with the radius of the common horizon given by a simple geometrical law. We also discuss the difference between the horizon and the apparent horizon in these analogue black holes with quantized constituents.
Paper Structure (7 sections, 6 equations, 3 figures)

This paper contains 7 sections, 6 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The model
  3. Single vortex as a black hole
  4. Vortex attraction
  5. Common horizon
  6. Radius of the horizon
  7. Discussion and conclusions

Figures (3)

  • Figure 1: Polariton quantum vortices as analogue black holes. a) Scheme of a quantum vortex with local flow velocity components. b) Radial velocity $|v_r|$ and speed of sound $c$ as functions of distance $r$ from the vortex center for different damping $\Lambda$. Varying $\Lambda$ allows to change the radius of the horizon. c) The inspiral phase for 2 and 8 vortices: relative center of mass vortex coordinate $r$ as a function of time $t$. Solid lines -- numerical simulations, dashed lines -- analytical solution.
  • Figure 2: Formation of a common horizon. a) A merger of 6 quantum vortices. Green dashed line -- static limit, black solid line -- $|v_r|=c$, blue line -- apparent horizon (Eq. \ref{['horeq']}). Vortex centers appear as blue dots. b,c) Simulation of possible trajectories on top of the background flow for 6 and 10 vortices. Arrows: background flow velocity in the rotating frame. Lines: possible trajectories (black -- infalling, red -- escaping). The true horizon appears as a boundary between red and black trajectories. In all panels, false color represents the polariton density (log scale).
  • Figure 3: Multiple-vortex black hole. a) Illustration for the link between the number of vortices and the radius of the horizon. b) Fine structure of the horizon explaining its modulation. c) Minimal radius of the apparent horizon and the static limit as a function of number of vortices. Black dots -- numerical simulations, solid lines -- analytical fits.