Counting a black hole in Lorentzian product triangulations

Dittrich, Bianca; Loll, R.

doi:10.1088/0264-9381/23/11/012

Cited by 38 publications

(71 citation statements)

References 34 publications

(171 reference statements)

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“…In some cases, the resulting models might then be reformulated as "tiling" models on a fixed lattice [30][31][32].…”

Section: Endnotesmentioning

confidence: 99%

“…Once one decides to sum over lattice structure, one must provide a prescription to do so. The class of triangulations to be summed over can be restricted, for instance, in order to implement causality [16,17,29] or to symmetry-reduce models [30][31][32]. 1 Another possibility is to ask for models which are per se lattice or discretization independent.…”

Section: Introductionmentioning

confidence: 99%

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Spin Foam Models with Finite Groups

2013

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Spin foam models, loop quantum gravity, and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity-inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community, we provide an introduction to some essential concepts in the loop quantum gravity, spin foam, and group field theory approach and point out the many connections to the lattice field theory and the condensed-matter systems.

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“…In some cases, the resulting models might then be reformulated as "tiling" models on a fixed lattice [30][31][32].…”

Section: Endnotesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spin Foam Models with Finite Groups

2013

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“…2. There are three different possibilities for how a tetrahedron can be oriented inside one of the prisms (see [23] for more geometric details). The apparent "straightness" of the towers is again an artefact of our representation, which emphasizes the product structure.…”

Section: Figurementioning

confidence: 99%

“…The entire two-dimensional triangulated spacetime can then be regarded as a fibration over a one-dimensional chain of links. More generally, product triangulations [23] are obtained by building towers over (arrays of) higherdimensional simplices, such as triangles. How a three-dimensional tower is built over a triangle is illustrated in Fig.2.…”

Section: Introducing the Model 21 The Product Type Triangulationsmentioning

confidence: 99%

(2+1)-dimensional quantum gravity as the continuum limit of causal dynamical triangulations

2007

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We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an additional notion of order on the discrete, causal geometries. This simplifies the combinatorial problem of counting geometries just enough to enable us to calculate the transfer matrix between boundary states labelled by the area of the spatial universe, as well as the corresponding quantum Hamiltonian of the continuum theory. This is the first time in dimension larger than two that a Hamiltonian has been derived from such a model by mainly analytical means, and opens the way for a better understanding of scaling and renormalization issues.

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“…Moreover, the simplifications occur approximately also for slowly evolving horizons [69] such that even dynamical situations are accessible. Alternatively, direct quantizations of classical expansion parameters have been formulated in [70,71,72] for fully dynamical situations.…”

Section: Quantum Horizonsmentioning

confidence: 99%

Quantum Geometry and Its Implications for Black Holes

Bojowald

2006

Int. J. Mod. Phys. D

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General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will provide a more complete, non-singular extension which, however, was difficult to verify in the absence of a quantum theory of gravity. By now there are several candidates which show essential hints as to what a quantum theory of gravity may look like. In particular, loop quantum gravity is a non-perturbative formulation which is background independent, two properties which are essential close to a classical singularity with strong fields and a degenerate metric. In cosmological and black hole settings one can indeed see explicitly how classical singularities are removed by quantum geometry: there is a well-defined evolution all the way down to, and across, the smallest scales. As for black holes, their horizon dynamics can be studied showing characteristic modifications to the classical behavior. Conceptual and physical issues can also be addressed in this context, providing lessons for quantum gravity in general. Here, we conclude with some comments on the uniqueness issue often linked to quantum gravity in some form or another.

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Counting a black hole in Lorentzian product triangulations

Cited by 38 publications

References 34 publications

Spin Foam Models with Finite Groups

Spin Foam Models with Finite Groups

(2+1)-dimensional quantum gravity as the continuum limit of causal dynamical triangulations

Quantum Geometry and Its Implications for Black Holes

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