Abstract
We identify the spectral properties of Hawking-Unruh radiation in the eternal black hole at ultra low energies as a probe for the chaotic level statistics of quantum black holes. Level repulsion implies that there are barely Hawking particles with an energy smaller than the level separation. This effect is experimentally accessible by probing the Unruh heat bath with a linear detector. We provide evidence for this effect via explicit and exact calculations in JT gravity building on a radar definition of bulk observables in the model. Similar results are observed for the bath energy density. This universal feature of eternal Hawking radiation should resonate into the evaporating setup.
Highlights
We identify the spectral properties of Hawking-Unruh radiation in the eternal black hole at ultra low energies as a probe for the chaotic level statistics of quantum black holes
If quantum gravity is quantum chaotic, what is the bulk gravitational interpretation of level repulsion and of random matrix level statistics? Recently this question has been addressed within Jackiw-Teitelboim (JT) gravity [11]
We conclude that any acceptable theory of quantum gravity in AdS is a discrete and unitary quantum system with random matrix level statistics
Summary
The main conceptual point in this work is that the semiclassical Planckian black body law for Hawking radiation does not take into account the chaotic level statistics of the quantum black holes which emit these quanta. The level density for the Unruh modes in the heat bath is by definition sensitive and proportional to the two-level spectral density ρ(E1, E2) of the underlying quantum black hole For this reason we expect that the intrinsically chaotic level statistics of quantum black holes modifies the detection formula (1.7) for the probability to detect a massless scalar Hawking particle with energy ω that has been emitted by a black hole with energy E as. This appropriately takes into account level repulsion..
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