# The Statistical Fingerprints of Quantum Gravity

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## Date

2008-09-29T19:14:40Z

## Authors

Ansari, Mohammad Hossein

## Journal Title

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## Volume Title

## Publisher

University of Waterloo

## Abstract

In this thesis some equilibrium and non-equilibrium statistical
methods are implied on two different versions of non-perturbative
quantum gravity.
Firstly, we report a novel statistical mechanics in which a class of evolutionary maps
act on trivalent spin network in randomly chosen initial states
and give rise to Self-organized Criticality. The result of continuously applying these maps indicate an expansion in the space-time area associated.
Secondly, a previously unknown statistical mechanics in quantum gravity is introduced in the framework of two dimensional Causal Dynamical Triangulations. This provides us a useful and new tools to understand this quantum gravity in terms of effective spins. This study reveals a correspondence between the statistics of Anti-ferromagnetic
systems and Causal Dynamical quantum gravity. More importantly, it provides a basis for studying anti-ferromagnetic systems in a background independent way.
Thirdly, two novel properties of area operator in
Loop Quantum Gravity are reported: 1) the generic degeneracy
and 2) the ladder symmetry. These were not known previously for years. The first one indicates that
corresponding to any eigenvalue of area operator in loop quantum gravity there exists a finite number of
degenerate eigenstates. This degeneracy is shown to be one way for the explanation of black hole entropy in a microscopic way. More importantly, we reproduce Bekenstein-Hawking entropy of black hole by comparing the minimal energy of a decaying frequency from a loop quantum black hole and the extracted energy from a perturbed black hole in the highly damping mode. This consistency reveals a treasure model for describing a black hole in loop quantum gravity that does nor suffer from the restrictions of an isolated horizon. The second property indicates there exists a ladder symmetry unexpectedly
in the complete spectrum of area eigenvalues. This symmetry suggests the eigenvalues of area could be classified into different evenly
spaced subsets, each called a `generation.' All generations are evenly
spaced; but the gap between the levels in any every generation is
unique. One application of the two new properties of area operator
have been considered here for introducing a generalized picture of
horizon whose area cells are not restricted to the subset considered
in quantum isolated horizon theory. Instead, the area cells accepts
values from the complete spectrum. Such horizon in the presence of
all elements of diffeomorphism group contains a number of degrees
of freedom independently from the bulk freedom whose logarithm
scales with the horizon area. Note that this is not the case in quantum isolated horizon when the complete elements of diffeomorphism
applies.
Finally, we use a simple statistical method in which no pre-assumption is made for the essence of the energy quanta radiated
from the hole. We derive the effects of the black hole horizon fluctuations and reveal a new phenomenon called "quantum amplification
effects" affecting black hole radiation. This effect causes unexpectedly a few un-blended radiance modes manifested in spectrum as
discrete brightest lines. The frequency of these modes scales with
the mass of black hole. This modification to Hawking's radiation
indicates a window at which loop quantum gravity can be observationally tested at least for primordial black holes.

## Description

## Keywords

Statistical Mechanics, Quantum Gravity