Optical analogue of the Schwarzschild-Planck metric

Abstract: We revisit the connection between trajectories of accelerated mirrors and spacetime metrics. We present the general (1+1)D effective metric that can be obtained with a fibre-optical analogue through the Kerr effect. Then we introduce a new connection between accelerated mirrors and the optical metric. In particular, we connect them for two specific trajectories: The first one is the black mirror that perfectly recreates the Schwarzchild spacetime. The second one is the Schwarzschild-Planck metric that is a regularized version of the Schwarzschild case. The regularization depends on a length scale that has a clear physical interpretation in the fibre-optical analogue system. We study the geometric properties and the Hawking radiation produced in these new analogue metrics.