Spherically symmetric quantum geometry: Hamiltonian constraint

Bojowald, Martin; Swiderski, Rafal

doi:10.1088/0264-9381/23/6/015

Cited by 138 publications

(219 citation statements)

References 101 publications

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“…Nevertheless, in a realistic collapsing scenario one has to employ a more general inhomogeneous setting (see Ref. [44,45] for recent development of techniques to handle inhomogeneous systems, which gives promising indications on how to extend the simpler homogeneous case). Furthermore, the effective theory that predicts a modified homogeneous dynamics, for the interior spacetime, may also modify the spacetime inhomogeneous structure [46].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Semiclassical dynamics of horizons in spherically symmetric collapse

Tavakoli

Marto

Dapor

2014

Int. J. Mod. Phys. D

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In this work, we consider a semiclassical description of the spherically symmetric gravitational collapse with a massless scalar field. In particular, we employ an effective scenario provided by holonomy corrections from loop quantum gravity, to the homogeneous interior spacetime. The singularity that would arise at the final stage of the corresponding classical collapse, is resolved in this context and is replaced by a bounce. Our main purpose is to investigate the evolution of trapped surfaces during this semiclassical collapse. Within this setting, we obtain a threshold radius for the collapsing shells in order to have horizons formation. In addition, we study the final state of the collapse by employing a suitable matching at the boundary shell from which quantum gravity effects are carried to the exterior geometry.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Semiclassical dynamics of horizons in spherically symmetric collapse

Tavakoli

Marto

Dapor

2014

Int. J. Mod. Phys. D

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“…In vacuum, for instance, a reduced quantization is possible [1,2,3]. This reduction has thus often been used in diverse approaches to quantum gravity, and also loop quantum gravity [4,5,6] has provided its own formulation [7,8,9,10,11]. This allows one to use the loop representation constructed in the full theory in a simpler setting in which, as one hopes, one can find and analyze physical solutions.…”

Section: Introductionmentioning

confidence: 99%

Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity

2008

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Lemaitre-Tolman-Bondi models as specific spherically symmetric solutions of general relativity simplify in their reduced form some of the mathematical ingredients of black hole or cosmological applications. The conditions imposed in addition to spherical symmetry turn out to take a simple form at the kinematical level of loop quantum gravity, which allows a discussion of their implications at the quantum level. Moreover, the spherically symmetric setting of inhomogeneity illustrates several nontrivial properties of lattice refinements of discrete quantum gravity. Nevertheless, the situation at the dynamical level is quite non-trivial and thus provides insights to the anomaly problem. At an effective level, consistent versions of the dynamics are presented which implement the conditions together with the dynamical constraints of gravity in an anomaly-free manner. These are then used for analytical as well as numerical investigations of the fate of classical singularities, including non-spacelike ones, as they generically develop in these models. None of the corrections used here resolve those singularities by regular effective geometries. However, there are numerical indications that the collapse ends in a tamer shell-crossing singularity prior to the formation of central singularities for mass functions giving a regular conserved mass density. Moreover, we find quantum gravitational obstructions to the existence of exactly homogeneous solutions within this class of models. This indicates that homogeneous models must be seen in a wider context of inhomogeneous solutions and their reduction in order to provide reliable dynamical conclusions.

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“…There is thus no tight prescription on how to obtain correction terms in perturbative situations. A further difference between our perturbative treatment here and the full theory is that we treat extrinsic curvature and the spin connection separately as it has been proven useful in homogeneous [18] and midi-superspace models [12,19]. This is not done in the full theory where one rather quantizes extrinsic curvature components in the constraint using [20].…”

Section: Discussionmentioning

confidence: 99%

Hamiltonian cosmological perturbation theory with loop quantum gravity corrections

et al. 2006

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Cosmological perturbation equations are derived systematically in a canonical scheme based on Ashtekar variables. A comparison with the covariant derivation and various subtleties in the calculation and choice of gauges are pointed out. Nevertheless, the treatment is more systematic when correction terms of canonical quantum gravity are to be included. This is done throughout the paper for one example of characteristic modifications expected from loop quantum gravity.

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Spherically symmetric quantum geometry: Hamiltonian constraint

Cited by 138 publications

References 101 publications

Semiclassical dynamics of horizons in spherically symmetric collapse

Semiclassical dynamics of horizons in spherically symmetric collapse

Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity

Hamiltonian cosmological perturbation theory with loop quantum gravity corrections

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