Holographic moving mirrors

TL;DR

The paper investigates holographic moving mirrors as tractable models for Hawking radiation and black hole information, using both 2D CFT field-theory analyses and AdS/BCFT gravity duals. By mapping moving-mirror profiles to static-boundary BCFTs and then to bulk AdS$_3$ geometries with end-of-the-world branes, the authors compute entanglement entropy holographically for escaping, kink, and double escaping mirrors, uncovering ideal Page curves and novel phase transitions. They connect these dynamics to 2D gravity on branes (Liouville theory) and to island-like pictures, showing how unitary entropy evolution can coexist with transient NEC violations and QNEC saturation. The work systematically relates conformal-map constructions, conformal field theory calculations, and holographic entanglement entropy, offering a unified framework to study information flow in evaporating black-hole analogs and non-equilibrium quantum systems. Overall, moving mirrors serve as a bridge between field theory, gravity, and quantum information, enabling explicit, controllable tests of unitarity, entanglement dynamics, and boundary-gravity interactions in a holographic setting.

Abstract

Moving mirrors have been known as tractable setups modeling Hawking radiation from black holes. In this paper, motivated by recent developments regarding the black hole information problem, we present extensive studies of moving mirrors in conformal field theories by employing both field theoretic as well as holographic methods. Reviewing first the usual field theoretic formulation of moving mirrors, we construct their gravity dual by resorting to the AdS/BCFT construction. Based on our holographic formulation, we then calculate the time evolution of entanglement entropy in various moving mirror models. In doing so, we mainly focus on three different setups: escaping mirror, which models constant Hawking radiation emanating from an eternal black hole; kink mirror, which models an evaporating black hole formed from collapse; and the double escaping mirror, which models two constantly radiating eternal black holes. In particular, by computing the holographic entanglement entropy, we show that the kink mirror gives rise to an ideal Page curve. We also find that an interesting phase transition arises in the case of the double escaping mirror. Furthermore, we argue and provide evidence for an interpretation of moving mirrors in terms of two dimensional Liouville gravity. We also discuss the connection between quantum energy conditions and the time evolution of holographic entanglement entropy in moving mirror models.

Figures (37)

• Figure 1: Sketch of the three moving mirror setups: (left) escaping mirror, (center) kink mirror, and (right) double escaping mirror. They model constant Hawking radiation, black hole formation and evaporation, and radiation from two black holes, respectively.
• Figure 2: Sketch of conformal map from the moving mirror setup (left) to a standard setup of BCFT with a straight line boundary at $\tilde{x} = 0$ (right). The dotted lines correspond to the null lines in the coordinates $(t,x)$ and $(\tilde{t}, \tilde{x})$.
• Figure 3: Depicted is the profile of the escaping mirror trajectory (left) and that of the energy stress tensor $T_{uu}(u)$ multiplied by $48\pi$ (right). The blue and orange curves correspond to $\beta=1$ and $\beta=0.3$, respectively.
• Figure 4: Shown is the profile of the kink mirror trajectory (left) and that of the energy stress tensor $T_{uu}(u)$ multiplied by $48\pi$ (right). We have set $u_0=4$. The blue and orange curves correspond to $\beta=0.5$ and $\beta=0.1$, respectively.
• Figure 5: Left: Penrose diagram of a black hole formed from a collapsing null shell (yellow thick line). This scenario may be modeled by the escaping mirror from Sec. \ref{['subsec:ex4']}. Right: Penrose diagram of the formation and evaporation of a black hole. This scenario may be modeled by the kink mirror from Sec. \ref{['subsubsec:double-kink-MM']}. The region behind the event horizon is colored in green.