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arXiv:2603.28030

Self-Reflection in a Moving Mirror

Michael R. R. Good, Eric V. Linder

gr-qcquant-phSubmitted Mar 30, 2026• Announced Mar 31, 2026
arXivHTMLPDF

Abstract

We present an analytic flat-spacetime accelerating boundary analog of Hawking-type emission that possesses infinite asymptotic acceleration (and radial acceleration in the black hole analog) but finite total radiated energy (and zero surface gravity in the black hole analog). We perform a unified study of its scattering symmetry, horizon formation, asymptotically extreme acceleration, finite total radiated energy, and the distinction between local energy flux and global particle production within a single closed-form model. The particle spectrum, energy spectrum, and equivalent spacetime metric are derived, revealing an interesting mix of normal and extremal black hole properties.

Journal reference
Classical and Quantum Gravity (2026)
DOI
10.1088/1361-6382/ae770f
Comments
11 pages, 4 figures

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Abstract. A microscopic description of Hawking radiation in sonic black holes has been recently presented [1]. This exactly solvable model is formulated in terms of onedimensional scattering of a Fermi gas. In this paper, the model is extended to account possible finite size effects of a realistic geometry. The flow of particles is maintained by a piston (i.e. an impenetrable barrier) moving slowly towards the sonic horizon. Using existing technologies the Hawking temperature can be of order of a few microkelvin in a realistic experiment.
We consider elongated condensates that cross twice the speed of sound. In the absence of periodic boundary conditions, the phonon spectrum possesses a discrete and finite set of complex frequency modes that induce a laser effect. This effect constitutes a dynamical instability and is due to the fact that the supersonic region acts as a resonant cavity. We numerically compute the complex frequencies and density–density correlation function. We obtain patterns with very specific signatures. In terms of the gravitational analogy, the flows we consider correspond to a pair of black hole and white hole horizons, and the laser effect can be conceived as self-amplified Hawking radiation. This is verified by comparing the outgoing flux at early time with the standard black hole radiation.
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