M\"obius Mirrors

TL;DR

This paper shows that a M"obius transformation applied to accelerating mirror trajectories preserves energy flux, particle spectrum, and entanglement entropy, enabling generation of diverse black hole analogs and horizon models.

Contribution

It introduces a M"obius transformation framework that maintains key physical invariants in accelerating mirror models, connecting various horizon and black hole analogs.

Findings

Energy flux and particle spectrum are invariant under M"obius transformations.

Generated families of trajectories include - and Schwarzschild black hole analogs.

The approach links different horizon models through geometric transformations.

Abstract

An accelerating boundary (mirror) acts as a horizon and black hole analog, radiating energy with some particle spectrum. We demonstrate that a M\"obius transformation on the null coordinate advanced time mirror trajectory uniquely keeps invariant not only the energy flux but the particle spectrum. We clarify how the geometric entanglement entropy is also invariant. The transform allows generation of families of dynamically distinct trajectories, including $\mathcal{PT}$-symmetric ones, mapping from the eternally thermal mirror to the de Sitter horizon, and different boundary motions corresponding to Kerr or Schwarzschild black holes.