Cosmological Effective Hamiltonian from full Loop Quantum Gravity Dynamics

Dapor, Andrea; Liegener, Klaus

doi:10.48550/arxiv.1706.09833

Cited by 35 publications

(75 citation statements)

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“…As a full theory of quantum gravity is not available, these are still open questions. In the case of cosmology, symmetry reduced models of loop quantum gravity (LQG), so called loop quantum cosmology (LQC), were able to describe spacetime in the Planck regime [6][7][8][9] (nevertheless note recent criticism [10]). Similar efforts have been taken within the framework of spherically symmetric and static black holes, which are still simple due to a high amount of symmetries.…”

Section: Introductionmentioning

confidence: 99%

Effective Quantum Dust Collapse via Surface Matching

Münch

2020

Preprint

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The fate of matter forming a black hole is still an open problem, although models of quantum gravity corrected black holes are available. In loop quantum gravity (LQG) models were presented, which resolve the classical singularity in the centre of the black hole by means of a black-to-white hole transition, but neglect the collapse process. The situation is similar in other quantum gravity approaches, where eternal non-singular models are available. In this paper, a strategy is presented to generalise these eternal models to dynamical collapse models by surface matching. Assuming 1) the validity of a static quantum black hole spacetime outside the collapsing matter, 2) homogeneity of the collapsing matter, and 3) differentiability at the surface of the matter fixes the dynamics of the spacetime uniquely. It is argued that these assumptions resemble a collapse of pressure-less dust and thus generalises the Oppenheimer-Snyder-Datt model, although no precise model of the matter has to be assumed. Hawking radiation is systematically neglected in this approach. The junction conditions and the spacetime dynamics are discussed generically for bouncing black hole spacetimes, as proposed by LQG, although the scheme is approach independent. Further, the equations are explicitly solved for the recent model [1] and a global spacetime picture of the collapse is achieved. The causal structure is discussed in detail and the Penrose diagram is constructed. The trajectory of the collapsing matter is completely constructed from an inside and outside observer point of view. The general analysis shows that the matter is collapsing and re-expanding and crosses the Penrose diagram diagonally. This way the infinite tower of Penrose diagrams, as proposed by several LQG models, is generically not cut out. Questions about different timescales of the collapse for in-and outside observers can be answered.

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Section: Introductionmentioning

confidence: 99%

Effective Quantum Dust Collapse via Surface Matching

Münch

2020

Preprint

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“…The most important effect caused by the holonomy correction is that the cosmological singularity is replaced by a bounce; and this result holds irrespective of the choice of quantization prescription, i.e. the bounce exists no matter we choose the standard holonomy quantization prescription in which the Euclidean term and Lorentz term of the Hamiltonian constraint are treated on the same footing [7,8] or the modified holonomy quantization in which the Euclidean term and Lorentz term are treated differently in the way which mimics the quantization prescription of the Hamiltonian constraint of loop quantum gravity [9][10][11]. Despite the uniform existence of bounce, different choice of holonomy quantization prescription can lead to essentially different behaviors in the effective dynamics.…”

Section: Introductionmentioning

confidence: 96%

Nonclassical cosmological dynamics in the low-energy limit of loop quantum scalar-tensor theory

Han

2021

Preprint

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“…Instead, the operator which we obtain is defined on the Hilbert space of a fixed cubical graph, and so it has to be interpreted in the context of some suitable framework or a model which is based on the formalism of full loop quantum gravity, but where the restriction to a cubical graph is taken as an assumption. Such models include quantum-reduced loop gravity [12][13][14] -a simplified model of loop quantum gravity, which is derived from the full theory through a procedure representing a gauge fixing to a diagonal densitized triad -and the effective dynamics approach [15][16][17], where the expectation value of the Hamiltonian with respect to a family of semiclassical states is considered as an effective Hamiltonian generating evolution on a classical phase space. From a more theoretical standpoint, algebraic quantum gravity [18,19] constitutes a framework in which the use of a single fixed graph (which one can take to be e.g.…”

Section: Introductionmentioning

confidence: 99%

Scalar curvature operator for models of loop quantum gravity on a cubical graph

Lewandowski¹,

Mäkinen²

2021

Preprint

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In this article we introduce a new operator representing the three-dimensional scalar curvature in loop quantum gravity. Our construction does not apply to the entire kinematical Hilbert space of loop quantum gravity; instead, the operator is defined on the Hilbert space of a fixed cubical graph. The starting point of our work is to write the spatial Ricci scalar classically as a function of the densitized triad. We pass from the classical expression to a quantum operator through a regularization procedure, in which spatial derivatives of the triad are discretized as finite differences on the cubical lattice provided by the graph. While more work is needed in order to extend our construction to encompass states based on all possible graphs, the operator presented here can be applied in models such as quantum-reduced loop gravity and effective dynamics, which are derived from the kinematical framework of full loop quantum gravity, and are formulated in terms of states defined on cubical graphs.

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Cosmological Effective Hamiltonian from full Loop Quantum Gravity Dynamics

Cited by 35 publications

References 0 publications

Effective Quantum Dust Collapse via Surface Matching

Effective Quantum Dust Collapse via Surface Matching

Nonclassical cosmological dynamics in the low-energy limit of loop quantum scalar-tensor theory

Scalar curvature operator for models of loop quantum gravity on a cubical graph

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