On Global Hyperbolicity of Spacetimes: Some Recent Advances and Open Problems

Finster, Felix; Much, Albert; Papadopoulos, Kyriakos

doi:10.1007/978-3-030-84721-0_15

Cited by 3 publications

(3 citation statements)

References 40 publications

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“…There are of course concrete proposals for non-commutative spacetimes, for example for Riemannian spectral triples [72], but the Lorentzian case presents extra challenges [73]. As was mentioned in the previous work [21], already for a classical Lorentzian manifold there can be a mismatch between the topology of the underlying manifold and the causal ordering induced by the Lorentzian metric [74], and we refer to the review [75] for an overview of results and open questions. A possible way to define the topology of such a quantum spacetime would be to start on the background spacetime with the path topology of Hawking, King and McCarthy [76] or one of its refinements [77][78][79], which includes the causal structure of the manifold.…”

Section: Discussionmentioning

confidence: 98%

Strict deformations of quantum field theory in de Sitter spacetime

Fröb

Much

2021

Journal of Mathematical Physics

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We show that a non-commutative structure arises naturally from perturbative quantum gravity in a de Sitter background metric. Our work builds on recent advances in the construction of observables in highly symmetric background spacetimes [Brunetti et al., JHEP 08, 032 (2016); Fröb and Lima, Class. Quant. Grav. 35, 095010 (2018)], where the dynamical coordinates that are needed in the relational approach were established for such backgrounds to all orders in perturbation theory. We show that these dynamical coordinates that describe events in the perturbed spacetime are naturally non-commuting, and determine their commutator to leading order in the Planck length. Our result generalizes the causal non-commutative structure that was found using the same approach in Minkowski space [Fröb, Much and Papadopoulos, Phys. Rev. D 107, 064041 (2023)].

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Section: Discussionmentioning

confidence: 98%

Strict deformations of quantum field theory in de Sitter spacetime

Fröb

Much

2021

Journal of Mathematical Physics

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“…In this regard, one important question that needs to be investigated further and clarified is the topology of a non-commutative spacetime, and in particular how causal orderings can be defined for arbitrary (not necessarily small) non-commutativity. There are of course concrete proposals, for example for Riemannian spectral triples [63], but the Lorentzian case presents extra challenges [64]: even for a classical Lorentzian manifold there can be a mismatch between the topology of the underlying manifold and the causal ordering induced by the Lorentzian metric [65]; see [66] for an overview of results and open questions. However, before tackling these foundational questions we first want to collect more information in concrete examples, and generalise our results to other interesting background spacetimes such as de Sitter or cosmological spacetimes, and possibly higher orders in perturbation theory.…”

Section: Discussionmentioning

confidence: 99%

Non-commutative Geometry from Perturbative Quantum Gravity

Fröb¹,

Much²,

Papadopoulos³

2022

Preprint

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Trying to connect a fundamentally non-commutative spacetime with the conservative perturbative approach to quantum gravity, we are led to the natural question: are non-commutative geometrical effects already present in the regime where perturbative quantum gravity provides a predictive framework? Moreover, is it necessary to introduce non-commutativity by hand, or does it arise through quantum-gravitational effects? We show that the first question can be answered in the affirmative, and the second one in the negative: perturbative quantum gravity predicts non-commutativity at the Planck scale, once one clarifies the structure of observables in the quantum theory.

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“…While there are some proposals (for example for Riemannian spectral triples [49]), this is a challenge especially in the Lorentzian case [50]. Already in the classical case, there can be a mismatch between the topology of the underlying manifold and the causal ordering induced by the Lorentzian metric [51]; see [52] for an overview of results and open questions.…”

Section: Pos(corfu2022)307mentioning

confidence: 99%

Non-commutative coordinates from quantum gravity

Fröb,

Much,

Papadopoulos

2023

Proceedings of Corfu Summer Institute 2022 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2022)

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Local observables in (perturbative) quantum gravity are notoriously hard to define, since the gauge symmetry of gravity -diffeomorphisms -moves points on the manifold. In particular, this is a problem for backgrounds of high symmetry such as Minkowski space or de Sitter spacetime which describes the early inflationary phase of our universe. Only recently this obstacle has been overcome, and a field-dependent coordinate system has been constructed to all orders in perturbation theory, in which observables are fully gauge-invariant. We show that these fielddependent coordinates are non-commutative, and compute their commutator to second order in the Planck length. This provides the first systematic derivation of non-commutativity that arises due to quantum gravity effects.

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On Global Hyperbolicity of Spacetimes: Some Recent Advances and Open Problems

Cited by 3 publications

References 40 publications

Strict deformations of quantum field theory in de Sitter spacetime

Strict deformations of quantum field theory in de Sitter spacetime

Non-commutative Geometry from Perturbative Quantum Gravity

Non-commutative coordinates from quantum gravity

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