Analogue black hole merger in a polariton condensate

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, gravitational 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 whose constituents exhibit topological quantization.