Acceleration radiation and HBAR thermodynamics for atoms falling into a BTZ black hole: A CQM quantum-optics approach

Abstract

Atoms falling freely into a Bañados-Teitelboim-Zanelli (BTZ) black hole in a Boulware-like vacuum are shown to emit radiation with a Planck spectrum at the Hawking temperature $T_{H}$. This leads to thermal Hawking-like radiation for a cloud of falling atoms prepared with random initial times. Moreover, the radiation is related to the relative equivalence principle, with the vacuum field modes accelerated with respect to the falling atom. The physics of the atom-field interactions is most easily described within a quantum optics approach, where each atom can be interpreted as a detector. Despite the topological nature of gravity in $(2+1)$ dimensions, the thermodynamic and radiation properties of BTZ black holes are still universally governed by the same near-horizon conformal quantum mechanics (CQM) applicable to higher-dimensional gravity. This universal conformal behavior is exhibited by all fields in the background of generic black holes, and generates an HBAR entropy $S_{\mathcal P}$ associated with the photon radiation field that mimics the Bekenstein-Hawking entropy $S_{\mathrm{BH}}=A/4$, proportional to the black-hole horizon area, and with the correct $1/4$ proportionality factor.