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Universe
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Beyond Riemannian Geometry in Classical and Quantum Gravity
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Beyond Riemannian Geometry in Classical and Quantum Gravity

A special issue of Universe (ISSN 2218-1997).

Deadline for manuscript submissions: closed (10 August 2022) | Viewed by 15460

Special Issue Editors

Dr. Marco Danilo Claudio Torri

E-Mail Website
Guest Editor
Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, I-20133 Milano, Italy
Interests: quantum gravity; general relativity; differential geometry; theoretical physics
Dr. Christian Pfeifer

E-Mail Website
Guest Editor
Center of Applied Space Technology and Microgravity (ZARM), University of Bremen, 28359 Bremen, Germany
Interests: general relativity; Finsler and hamilton geometry; quantum gravity phenomenology; modified dispersion relations; modified gravity teleparallel gravity; the geometry of gauge theories and fibre bundles; classical and quantum premetric electrodynamics
Dr. Nicoleta Voicu

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, Faculty of Mathematics and Computer Science, Transilvania University of Brasov, 500091 Brasov, Romania
Interests: Finsler geometry and applications; calculus of variations on manifolds; extended theories of gravity

Special Issue Information

Dear Colleagues,

The beneficial interaction of mathematics and physics can particularly be seen in the use of geometry in theoretical physics, where geometric concepts are well established. The geometry of principle bundles describes gauge field theories in the standard model of particle physics as well as in the study of the properties of media in solid-state physics, while in the framework of general relativity the gravitational interaction is identified with the semi-Riemannian (Lorentzian) geometry of spacetime.

The identification of spacetime geometry and gravity leads directly to the question of whether further geometric frameworks exist which could improve the description of gravity compared to Lorentzian geometry, in view of the still-missing self-consistent quantization of gravity and unexplained phenomena such as dark energy and dark matter.

This Special Issue aims to assemble an overview of the use of geometric concepts which go beyond semi-Riemannian geometry in their description of classical and quantum gravity.

We welcome contributions which present a review of different geometric concepts and their application to gravitational physics as well as new research articles and essays on the relation between gravity and geometry.

Dr. Marco Danilo Claudio Torri
Dr. Christian Pfeifer
Dr. Nicoleta Voicu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Universe is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

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Published Papers (7 papers)

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Research

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15 pages, 324 KiB  
Article
Black Hole Surface Gravity in Doubly Special Relativity Geometries
by José Javier Relancio and Stefano Liberati
Universe 2022, 8(2), 136; https://doi.org/10.3390/universe8020136 - 21 Feb 2022
Cited by 8 | Viewed by 1877
Abstract
In a quantum gravity theory, spacetime at mesoscopic scales can acquire a novel structure very different from the classical concept of general relativity. A way to effectively characterize the quantum nature of spacetime is through a momentum dependent space-time metric. There is a [...] Read more.
In a quantum gravity theory, spacetime at mesoscopic scales can acquire a novel structure very different from the classical concept of general relativity. A way to effectively characterize the quantum nature of spacetime is through a momentum dependent space-time metric. There is a vast literature showing that this geometry is related to relativistic deformed kinematics, which is precisely a way to capture residual effects of a quantum gravity theory. In this work, we study the notion of surface gravity in a momentum dependent Schwarzschild black hole geometry. We show that using the two main notions of surface gravity in general relativity we obtain a momentum independent result. However, there are several definitions of surface gravity, all of them equivalent in general relativity when there is a Killing horizon. We show that in our scheme, despite the persistence of a Killing horizon, these alternative notions only agree in a very particular momentum basis, obtained in a previous work, so further supporting its physical relevance. Full article
(This article belongs to the Special Issue Beyond Riemannian Geometry in Classical and Quantum Gravity)
8 pages, 271 KiB  
Article
The Laplace Transform of Quantum Gravity
by Jorge Gamboa, Fernando Méndez and Natalia Tapia-Arellano
Universe 2022, 8(2), 116; https://doi.org/10.3390/universe8020116 - 12 Feb 2022
Viewed by 2318
Abstract
Following analogies with relativistic point particles and Schild strings, we show that the Einstein gravity and its strong coupling regime (or the Planck mass going to zero) are related to each other through a Laplace transform. The Feynman propagator of gravity in the [...] Read more.
Following analogies with relativistic point particles and Schild strings, we show that the Einstein gravity and its strong coupling regime (or the Planck mass going to zero) are related to each other through a Laplace transform. The Feynman propagator of gravity in the strong coupling regime satisfies a functional diffusion equation in the three-metric space with the evolution parameter being the volume of spacetime. We conjecture that the relationship between both regimes is consistent with the existence of an evolution operator in which time is replaced by the volume of spacetime. Full article
(This article belongs to the Special Issue Beyond Riemannian Geometry in Classical and Quantum Gravity)
13 pages, 1534 KiB  
Article
Diffeomorphisms in Momentum Space: Physical Implications of Different Choices of Momentum Coordinates in the Galilean Snyder Model
by Giulia Gubitosi and Salvatore Mignemi
Universe 2022, 8(2), 108; https://doi.org/10.3390/universe8020108 - 9 Feb 2022
Cited by 6 | Viewed by 1491
Abstract
It has been pointed out that different choices of momenta can be associated to the same noncommutative spacetime model. The question of whether these momentum spaces, related by diffeomorphisms, produce the same physical predictions is still debated. In this work, we focus our [...] Read more.
It has been pointed out that different choices of momenta can be associated to the same noncommutative spacetime model. The question of whether these momentum spaces, related by diffeomorphisms, produce the same physical predictions is still debated. In this work, we focus our attention on a few different momentum spaces that can be associated to the Galilean Snyder noncommutative spacetime model and show that they produce different predictions for the energy spectrum of the harmonic oscillator. Full article
(This article belongs to the Special Issue Beyond Riemannian Geometry in Classical and Quantum Gravity)
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33 pages, 484 KiB  
Article
On the Significance of the Stress–Energy Tensor in Finsler Spacetimes
by Miguel Ángel Javaloyes, Miguel Sánchez and Fidel F. Villaseñor
Universe 2022, 8(2), 93; https://doi.org/10.3390/universe8020093 - 31 Jan 2022
Cited by 5 | Viewed by 1993
Abstract
We revisit the physical arguments that led to the definition of the stress–energy tensor T in the Lorentz–Finsler setting (M,L) starting with classical relativity. Both the standard heuristic approach using fluids and the Lagrangian one are taken into account. [...] Read more.
We revisit the physical arguments that led to the definition of the stress–energy tensor T in the Lorentz–Finsler setting (M,L) starting with classical relativity. Both the standard heuristic approach using fluids and the Lagrangian one are taken into account. In particular, we argue that the Finslerian breaking of Lorentz symmetry makes T an anisotropic 2-tensor (i.e., a tensor for each L-timelike direction), in contrast with the energy-momentum vectors defined on M. Such a tensor is compared with different ones obtained by using a Lagrangian approach. The notion of divergence is revised from a geometric viewpoint, and, then, the conservation laws of T for each observer field are revisited. We introduce a natural anisotropic Lie bracket derivation, which leads to a divergence obtained from the volume element and the non-linear connection associated with L alone. The computation of this divergence selects the Chern anisotropic connection, thus giving a geometric interpretation to previous choices in the literature. Full article
(This article belongs to the Special Issue Beyond Riemannian Geometry in Classical and Quantum Gravity)
18 pages, 681 KiB  
Article
f(T, B) Cosmography for High Redshifts
by Celia Escamilla-Rivera, Geovanny Rave-Franco and Jackson Levi-Said
Universe 2021, 7(11), 441; https://doi.org/10.3390/universe7110441 - 16 Nov 2021
Cited by 9 | Viewed by 2010
Abstract
In light of the statistical performance of cosmological observations, in this work we present the cosmography in f(T,B) gravity. In this scenario we found a cosmological viable standard case that allows the reduction of the degeneracy between several [...] Read more.
In light of the statistical performance of cosmological observations, in this work we present the cosmography in f(T,B) gravity. In this scenario we found a cosmological viable standard case that allows the reduction of the degeneracy between several f(T,B) models already proposed in the literature. Furthermore, we constrain this model using Pantheon SNeIa compilation, cosmic chronometers and a newly GRB calibrated data sample. We found that with an appropriate strategy for including the cosmographic parameter, we do produce a viable cosmology with our model within f(T,B) gravity. Full article
(This article belongs to the Special Issue Beyond Riemannian Geometry in Classical and Quantum Gravity)
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Review

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43 pages, 865 KiB  
Review
Torsion in String-Inspired Cosmologies and the Universe Dark Sector
by Nick E. Mavromatos
Universe 2021, 7(12), 480; https://doi.org/10.3390/universe7120480 - 6 Dec 2021
Cited by 16 | Viewed by 2958
Abstract
Several aspects of torsion in string-inspired cosmologies are reviewed. In particular, its connection with fundamental, string-model independent, axion fields associated with the massless gravitational multiplet of the string are discussed. It is argued in favour of the role of primordial gravitational anomalies coupled [...] Read more.
Several aspects of torsion in string-inspired cosmologies are reviewed. In particular, its connection with fundamental, string-model independent, axion fields associated with the massless gravitational multiplet of the string are discussed. It is argued in favour of the role of primordial gravitational anomalies coupled to such axions in inducing inflation of a type encountered in the “Running-Vacuum-Model (RVM)” cosmological framework, without fundamental inflaton fields. The gravitational-anomaly terms owe their existence to the Green–Schwarz mechanism for the (extra-dimensional) anomaly cancellation, and may be non-trivial in such theories in the presence of (primordial) gravitational waves at early stages of the four-dimensional string universe (after compactification). The paper also discusses how the torsion-induced stringy axions can acquire a mass in the post inflationary era, due to non-perturbative effects, thus having the potential to play the role of (a component of) dark matter in such models. Finally, the current-era phenomenology of this model is briefly described with emphasis placed on the possibility of alleviating tensions observed in the current-era cosmological data. A brief phenomenological comparison with other cosmological models in contorted geometries is also made. Full article
(This article belongs to the Special Issue Beyond Riemannian Geometry in Classical and Quantum Gravity)
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Other

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10 pages, 1040 KiB  
Essay
Listening to Celestial Algebras
by Jose Beltrán Jiménez and Tomi S. Koivisto
Universe 2022, 8(8), 407; https://doi.org/10.3390/universe8080407 - 3 Aug 2022
Cited by 3 | Viewed by 1303
Abstract
In this essay, we immerse into the framework of normed division algebras as a suitable arena to accommodate the standard model of elementary particles, and we explore some applications to cosmology. Remarkably, they permit interesting non-trivial realisations of the cosmological principle with an [...] Read more.
In this essay, we immerse into the framework of normed division algebras as a suitable arena to accommodate the standard model of elementary particles, and we explore some applications to cosmology. Remarkably, they permit interesting non-trivial realisations of the cosmological principle with an interplay between the symmetry groups of the quaternions and octonions. We also argue how these realisations give rise to potentially observational signatures in gravitational waves astronomy. Full article
(This article belongs to the Special Issue Beyond Riemannian Geometry in Classical and Quantum Gravity)
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