Horizon brightened acceleration radiation entropy in causal diamond geometry: A near-horizon perspective

TL;DR

This work generalizes horizon brightened acceleration radiation (HBAR) to the causal diamond (CD) spacetime, showing that randomly injected freely falling atoms interacting with a scalar field yield a Planckian emission spectrum at $T_D = 1/(π α)$, governed by an emergent conformal quantum mechanics (CQM) near the CD horizons. The radiation-field density matrix is thermal, with a steady-state form $ρ^{(SS)} ∝ e^{-β ω n}$ and entropy flux obeying $\dot{S} = β_D \dot{E}$, where $β_D = π α$, linking thermodynamics to the CD’s causal structure via the partition function $Z(β) = ∏_j [1 - e^{-β ω_j}]^{-1}$. The results imply that causal horizons act as a topological thermal reservoir, with thermality arising from global causal structure rather than microscopic microdegrees of freedom, extending HBAR beyond black holes. This framework opens avenues for quantum thermodynamics and entropy production studies in finite-lifetime spacetimes and other causal-horizon geometries.

Abstract

In this article, we extend the horizon brightened acceleration radiation (HBAR) framework, originally introduced by Marlan Scully et al. in Proceedings of the National Academy of Sciences 115, 8131 (2018), to the causal diamond (CD) spacetime. We study a cloud of two-level atoms, injected at random times in the asymptotic past of the CD, freely falling toward its causal horizon and emitting scalar radiation via a weak dipole coupling to a quantum field. In the near-horizon region, an emergent conformal symmetry-captured by conformal quantum mechanics (CQM)-governs the field dynamics and allows analytic control of the emission process. We find that the radiation spectrum is thermal, with temperature $T_D = 1/(πα)$, and that the associated von Neumann entropy flux reproduces the entropy production of the radiation field. These results demonstrate that the causal horizons of the CD spacetime effectively act as a topological thermal reservoir, with thermal properties arising entirely from the global causal structure rather than from underlying microscopic degrees of freedom, highlighting that the validity of the HBAR framework is fundamentally tied to the existence of causal horizons, independent of the presence of a black hole.

Figures (7)

• Figure 1: (a) The causal diamond $D_R$ defined as the intersection of a future and a past light cone. (b) Uniformly accelerated trajectories in the right Rindler wedge.
• Figure 2: Constant-$\rho$ trajectories in the causal diamond $D_R$ for (a) $\rho \ll 1$, and (b) $\rho \gg 1$.
• Figure 3: (a) causal horizons at the left boundary of $D_R$. (b) causal horizons at the right boundary of $D_R$.
• Figure 4: (a) asymptotic regions of the CD spacetime represented by the four corners of the causal diamond $D_R$. (b) representation of the extended view of the corners in $D_R$
• Figure 5: (a) Geometric flow generated by the conformal Killing vector $\partial_\eta$ in the extended Minkowski geometry. (b) Normal vectors to the horizons of the region $D_R$.