Optical analogue of the Schwarzschild-Planck metric

TL;DR

This paper explores how fibre-optical systems can simulate spacetime metrics, specifically the Schwarzschild and Schwarzschild-Planck metrics, and investigates their geometric properties and Hawking radiation effects.

Contribution

It introduces a novel connection between accelerated mirrors and optical metrics, including a regularized Schwarzschild-Planck metric in fibre-optical analogues.

Findings

Successfully models Schwarzschild and Schwarzschild-Planck metrics optically.

Analyzes Hawking radiation in the new analogue metrics.

Provides a physical interpretation of the regularization length scale.

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.