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Fundamental Structure of Loop Quantum Gravity
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In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to practitioners to gain insights from different perspectives on the theory. We will focus on the theoretical framework itself, rather than its applications, and do our best to write it in modern and precise langauge while keeping the presentation accessible for beginners. After reviewing the classical connection dynamical formalism of general relativity, as a foundation, the construction of kinematical Ashtekar-Isham-Lewandowski representation is introduced in the content of quantum kinematics. The algebraic structure of quantum kinematics is also discussed. In the content of quantum dynamics, we mainly introduce the construction of a Hamiltonian constraint operator and the master constraint project. At last, some applications and recent advances are outlined. It should be noted that this strategy of quantizing gravity can also be extended to obtain other background independent quantum gauge theories. There is no divergence within this background independent and diffeomorphism invariant quantization programme of matter coupled to gravity.
Forward citations
Cited by 5 Pith papers
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Dust shell in effective loop quantum black hole model
In a polymerized loop-quantum-gravity black hole model, a collapsing dust shell bounces and, for sufficiently heavy shells, follows a spacelike trajectory through the horizon, implying a finite horizon lifetime and a ...
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Higher-dimensional quantum-corrected Oppenheimer-Snyder model with a cosmological constant
Extends quantum Oppenheimer-Snyder collapse model to higher dimensions plus cosmological constant and reports modified AdS black-hole thermodynamics with finite small-black-hole temperature and an extra quantum-induce...
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Echoes and quasinormal modes for static loop quantum black bounces
Scalar perturbations of the loop quantum black bounce spacetime produce echoes in traversable-wormhole configurations with a double-barrier effective potential, but not in regular-black-hole configurations with a sing...
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The quasinormal modes of the rotating quantum corrected black holes
The work calculates scalar quasinormal mode spectra for a rotating quantum-corrected black hole and constructs a methodological pipeline to infer the quantum correction parameter from gravitational-wave ringdown data ...
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Image of a quantum-corrected black hole without Cauchy horizons illuminated by a static thin accretion disk
For the no-Cauchy-horizon quantum-corrected metric, a larger quantum parameter produces larger horizon, photon sphere, ISCO, and shadow, with narrower and tighter-spaced photon and lensed rings.
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