Relativistic dynamics of moving mirrors in CFT$_2$: quantum backreaction and black holes

TL;DR

This paper models the dynamics of moving mirrors in 2D conformal field theories, showing how quantum backreaction influences mirror trajectories and prevents horizon formation, with implications for black hole physics.

Contribution

It introduces a self-consistent relativistic model of moving mirrors in CFT$_2$ that accounts for quantum backreaction and black hole analogs, extending prior fixed-trajectory analyses.

Findings

Quantum backreaction prevents mirror trajectories from forming horizons.

Mirror orbits can correspond to extremal black holes.

The model maintains finite velocities even in horizon-forming scenarios.

Abstract

There is a well-known correspondence between the physics of black hole evaporation and that of moving mirrors in QFT. However, most analyses in this subject rely on prescribed mirror trajectories. Here, we study the flat-space dynamics of $1+1$-dimensional Conformal Field Theories interacting with a relativistic boundary particle of mass $m$ acting as a perfect mirror. The trajectory of the latter is not fixed but follows its own relativistic equation of motion $F^\mu=ma^\mu$. For given initial conditions at past null infinity, we find the boundary particle's trajectory and the reflected energy-momentum of the quantum fields. For incoming vacuum states, the solution yields mirror orbits that correspond to extremal black holes. For the class of incoming states that produce orbits becoming null in finite proper time -- corresponding to the formation of a horizon -- at the classical level, the quantum backreaction avoids this endpoint rendering the mirror's velocity in lightcone coordinates finite. We investigate the behavior of the Averaged Null Energy Condition, which in this setup reduces to a boundary term.