Mirror Reflections of a Black Hole

TL;DR

This paper establishes a precise analogy between black hole formation and accelerating mirror dynamics in flat spacetime, analyzing spectral and energy flux properties to understand their thermodynamic behavior.

Contribution

It demonstrates an exact correspondence between black hole and accelerating mirror models for scalar fields, extending the analysis to higher dimensions and computing spectral and flux dynamics.

Findings

Spectral dynamics are similar in both models.

Energy flux approaches equilibrium monotonically.

Identifies a specific time when the system is most out-of-equilibrium.

Abstract

An exact correspondence between a black hole and an accelerating mirror is demonstrated. It is shown that for a massless minimally coupled scalar field the same Bogolubov coefficients connecting the "in" and "out" states occur for a (1+1)D flat spacetime with a particular perfectly reflecting accelerating boundary trajectory and a (1+1)D curved spacetime in which a null shell collapses to form a black hole. Generalization of the latter to the (3+1)D case is discussed. The spectral dynamics is computed in both (1+1)-dimensional spacetimes along with the energy flux in the spacetime with a mirror. It is shown that the approach to equilibrium is monotonic, asymmetric in terms of the rate, and there is a specific time which characterizes the system when it is the most out-of-equilibrium.