Quantum gravity is among the most fascinating problems in physics. It modifies our understanding of time, space and matter. The recent development of the loop approach has allowed us to explore domains ranging from black hole thermodynamics to the early Universe. This book provides readers with a simple introduction to loop quantum gravity, centred on its covariant approach. It focuses on the physical and conceptual aspects of the problem and includes the background material needed to enter this lively domain of research, making it ideal for researchers and graduate students. Topics covered include quanta of space; classical and quantum physics without time; tetrad formalism; Holst action; lattice QCD; Regge calculus; ADM and Ashtekar variables; Ponzano-Regge and Turaev-Viro amplitudes; kinematics and dynamics of 4D Lorentzian quantum gravity; spectrum of area and volume; coherent states; classical limit; matter couplings; graviton propagator; spinfoam cosmology and black hole thermodynamics.
A star that collapses gravitationally can reach a further stage of its life, where quantum-gravitational pressure counteracts weight. The duration of this stage is very short in the star proper time, yielding a bounce, but extremely long seen from the outside, because of the huge gravitational time dilation. Since the onset of quantum-gravitational effects is governed by energy density -not by size-the star can be much larger than planckian in this phase. The object emerging at the end of the Hawking evaporation of a black hole can then be larger than planckian by a factor (m/mP ) n , where m is the mass fallen into the hole, mP is the Planck mass, and n is positive. We consider arguments for n = 1/3 and for n = 1. There is no causality violation or faster-than-light propagation. The existence of these objects alleviates the black-hole information paradox. More interestingly, these objects could have astrophysical and cosmological interest: they produce a detectable signal, of quantum gravitational origin, around the 10 −14 cm wavelength.Measuring effects of the quantum nature of gravity is notoriously difficult [1,2], because of the smallness of the Planck scale. Here we suggest that cosmic rays in the GeV range might contain a trace of a quantum gravitational phenomenon. The large gap between this energy and the Planck energy could be bridged by a large multiplicative factor appearing because of the long (cosmological) lifetime of radiating primordial black holes. This could lead to measurements of "quantum gravity in the sky" [3]. This possibility is suggested by the existence of an apparent paradox currently widely discussed in the theoretical literature. Briefly: what is the fate of the information fallen into the hole, after it evaporates via Hawking radiation? Theoretical arguments appear to indicate that the information being carried out by the radiation implies unpalatable phenomena like "firewalls" [4,5]. But if information remains trapped inside, the final stage of the black hole at the end of the evaporation would have to store an amount of information hardly compatible with its expected planckian size [6][7][8]. A possible way out from these unsavory alternatives, suggested by Giddings [9], is that the size of the black hole at the final stage of the evaporation is much larger than planckian (see also [10,11]).Here we observe that this scenario does not require superluminal transfer of information and can follow from the fact that quantum gravitation phenomena become relevant when the matter energy density reaches the Planck scale, and this may happen at length scales much larger than planckian. Quantum gravity may liberate the information stored in the black hole when this is still large compared to the Planck length, implying the existence of a new phase in the life of gravitationally collapsed object [12], which could be short in proper time, but, due to gravitational time dilation, very long for an external observer. This, together with the hypothesis of primordial black holes, opens the possibi...
We compute the transition amplitude between coherent quantum-states of geometry peaked on homogeneous isotropic metrics. We use the holomorphic representations of loop quantum gravity and the Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at first order in the vertex expansion, second order in the graph (multipole) expansion, and first order in volume −1 . We show that the resulting amplitude is in the kernel of a differential operator whose classical limit is the canonical hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an indication that the dynamics of loop quantum gravity defined by the new vertex yields the Friedmann equation in the appropriate limit.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.