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Loop Quantum Gravity
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The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a mathematically well-defined, non-perturbative and background independent quantization of general relativity, with its conventional matter couplings. The research in loop quantum gravity forms today a vast area, ranging from mathematical foundations to physical applications. Among the most significative results obtained are: (i) The computation of the physical spectra of geometrical quantities such as area and volume; which yields quantitative predictions on Planck-scale physics. (ii) A derivation of the Bekenstein-Hawking black hole entropy formula. (iii) An intriguing physical picture of the microstructure of quantum physical space, characterized by a polymer-like Planck scale discreteness. This discreteness emerges naturally from the quantum theory and provides a mathematically well-defined realization of Wheeler's intuition of a spacetime ``foam''. Long standing open problems within the approach (lack of a scalar product, overcompleteness of the loop basis, implementation of reality conditions) have been fully solved. The weak part of the approach is the treatment of the dynamics: at present there exist several proposals, which are intensely debated. Here, I provide a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.
Forward citations
Cited by 11 Pith papers
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The emergent Big Bang scenario
A clock field interacting with matter in a Riemannian 4D space creates emergent Lorentzian patches, replacing the Big Bang singularity with a smooth signature-flip boundary and allowing an almost de Sitter early phase.
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A matrix free action of the Ashtekar-Lewandowski volume operator of loop quantum gravity
Develops a matrix-free SRQ-based action for the AL volume operator that exactly preserves the kernel and supports large-scale Monte Carlo and spectral estimates without dense matrices.
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Spherically symmetric solutions in quasi-local Einstein-Weyl gravity
In quasi-local Einstein-Weyl gravity, static spherically symmetric Frobenius solutions are classified: regular cores only, Schwarzschild-like horizons and wormhole throats, plus asymptotic 1/r^6 corrections to Schwarzschild.
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Emergent Thiemann coherent states in the near-kernel sector of quantum reduced loop gravity
Variational minimization of the squared Hamiltonian constraint in a truncated one-vertex loop gravity model yields three classes of near-kernel states; one factorized branch matches reduced Thiemann coherent states wi...
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Singularities in loop quantum cosmology
Loop quantum cosmology models harbor physical singularities or inconsistent space-time structures, with a new effective Friedmann equation revealing a sub-Planckian bounce after a singularity at infinite scale factor ...
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Consistency in the Quantum-Improved Charged Black Holes
Thermodynamic consistency for quantum-improved Reissner-Nordström black holes permits arbitrary radial dependence in both Newton and electromagnetic couplings, while equation-action consistency requires an extra quant...
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Quantum-Gravitational Backreaction in the BTZ Background from Curved Momentum Space
A semiclassical deformed BTZ solution encodes Planck-scale kinematic modifications from curved momentum space in a nonlinear microscopic-to-ADM mass map, leaving local geometry and thermodynamics unchanged in form.
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A Breakdown Case Study of the Lindblad Approach via Entanglement and Purity
A two-qubit system in a random many-body environment decoheres with two successive Gaussian decays, which a time-homogeneous Lindblad equation can never reproduce because its short-time decay is always linear.
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Noncommutative black holes: Topological bulk-boundary correspondence and Binary Merger Bounds
For noncommutative RN-AdS black holes, the paper claims bulk and boundary thermodynamic topological charges equal to zero and derives perturbative second-law corrections to the remnant-mass bound.
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Decay of uniformly rotating particles
Uniformly rotating particles decay via emission of negative-energy quanta due to the lack of a global vacuum for such observers, implying none can be regarded as stable.
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Aspects of the Black Hole Interior Volume and Entropy
A doctoral thesis compiles and reproduces prior semiclassical results claiming the interior scalar-mode entropy of black holes is proportional to horizon entropy with a coefficient less than one.
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