Similarities in the evaporation of saturated solitons and black holes

TL;DR

The paper investigates whether black-hole-like features are universal to saturons by studying a calculable 1+1D saturated SU(N) vacuum bubble coupled to massless fermions. It develops both a semiclassical and a fully quantum (corpuscular) description of evaporation, deriving the emission spectrum and rate, and establishing a Page-like information-retrieval timescale in the presence of memory-burden effects. The key results show Hawking-like evaporation with decay rate $\Gamma\sim \frac{1}{R}$ and quanta energy $E\sim \frac{1}{R}$, with information recoverability governed by $t_{ m Page}\sim S\,R$, and demonstrate exact agreement between semiclassical and quantum pictures in the appropriate large-$N$ limit. Together, these findings reinforce the view that black-hole properties are manifestations of universal saturation physics, supporting the idea of black holes as saturated coherent states of gravitons (the N-portrait) in a broader QFT context.

Abstract

It has been suggested some time ago that many black hole properties are not specific to gravity, but rather are shared by a large class of objects, the so-called saturons, that saturate the quantum field theoretic upper bound on microstate degeneracy. By now, various aspects of this universality have been understood and demonstrated in a number of explicit examples. In the present paper, we add one more brick to the building by showing that the decay of a simple two-dimensional saturated soliton copies some key aspects of the black hole decay as well as of the information retrieval. In particular, we study the evaporation process of a classically-stable vacuum bubble of a spontaneously broken $SU(N)$-symmetry, coupled to massless fermions. We show that the decay rate as well as the characteristic energy of the emitted quanta are given by the inverse size of the object, in striking similarity with the Hawking evaporation of a black hole. The time-scale of information retrieval also matches the one previously suggested for a black hole by Page. We give the semiclassical derivation of the phenomenon as well as its fully quantum resolution as a decaying coherent state of Goldstone bosons. The universal nature of the effect and its microscopic understanding support the analogous quantum portrait of a black hole as a saturated coherent state of gravitons.

Figures (7)

• Figure 1: The effective potential for the $\phi$ field. The bubble solution corresponds to the field "rolling" down from the zero value at "time" $r=\infty$ to the finite value $\phi_0$ at "time" $r=0$, and back to $\phi=0$.
• Figure 2: The bubble profile for the $\phi$ field.
• Figure 3: Possible regimes for a thin-wall bubble.
• Figure 4: Possible regimes for a thick-wall bubble.
• Figure 5: The dominant channel that leads to the bubble evaporation.