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Keywords = teleparallel geometry

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19 pages, 322 KB  
Article
Weak Gravity Limit in Newer General Relativity
by Alexey Golovnev, Sofia Klimova, Alla N. Semenova and Vyacheslav P. Vandeev
Universe 2025, 11(5), 149; https://doi.org/10.3390/universe11050149 - 3 May 2025
Cited by 1 | Viewed by 482
Abstract
We analyse linearised field equations around the Minkowski metric, with its standard flat parallel transport structure, in models of newer GR, which refers to quadratic actions in terms of a nonmetricity tensor. We show that half of the freedom in choosing the model [...] Read more.
We analyse linearised field equations around the Minkowski metric, with its standard flat parallel transport structure, in models of newer GR, which refers to quadratic actions in terms of a nonmetricity tensor. We show that half of the freedom in choosing the model parameters is immediately fixed by asking for reasonable properties of tensors and vectors, defined with respect to spatial rotations, and we accurately describe the much more complicated sector of scalars. In particular, we show that, from the teleparallel viewpoint, the STEGR model with an additional term of a gradient squared of the metric determinant exhibits one and a half new dynamical modes, and not just one new dynamical mode as it was previously claimed. Full article
(This article belongs to the Special Issue Geometric Theories of Gravity)
14 pages, 332 KB  
Article
Teleparallel Robertson-Walker Geometries and Applications
by Alan Albert Coley, Alexandre Landry and Fateme Gholami
Universe 2023, 9(10), 454; https://doi.org/10.3390/universe9100454 - 21 Oct 2023
Cited by 12 | Viewed by 1621
Abstract
In teleparallel geometries, the coframe and corresponding spin connection are the principal geometric objects and, consequently, the appropriate definition of a symmetry is that of an affine symmetry. The set of invariant coframes and their corresponding spin connections that respect the full six [...] Read more.
In teleparallel geometries, the coframe and corresponding spin connection are the principal geometric objects and, consequently, the appropriate definition of a symmetry is that of an affine symmetry. The set of invariant coframes and their corresponding spin connections that respect the full six dimensional Lie algebra of Robertson–Walker affine symmetries are displayed and discussed. We will refer to such geometries as teleparallel Robertson–Walker (TRW) geometries, where the corresponding derived metric is of Robertson–Walker form and is characterized by the parameter k=(1,0,1). The field equations are explicitly presented for the F(T) class of teleparallel TRW spacetimes. We are primarily interested in investigating the k0 TRW models. After first studying the k=0 models and, in particular, writing their governing field equations in an appropriate form, we then study their late time stability with respect to perturbations in k in both the cases of a vanishing and non-vanishing effective cosmological constant term. As an illustration, we consider both quadratic F(T) theories and power-law solutions. Full article
(This article belongs to the Special Issue Mathematical Cosmology)
27 pages, 407 KB  
Article
Teleparallel Minkowski Spacetime with Perturbative Approach for Teleparallel Gravity on a Proper Frame
by Alexandre Landry and Robert J. van den Hoogen
Universe 2023, 9(5), 232; https://doi.org/10.3390/universe9050232 - 15 May 2023
Cited by 6 | Viewed by 1582
Abstract
A complete perturbation theory suitable for teleparallel gravity is developed. The proposed perturbation scheme takes into account perturbations of the coframe, the metric, and the spin-connection, while ensuring that the resulting perturbed system continues to describe a teleparallel gravity situation. The resulting perturbation [...] Read more.
A complete perturbation theory suitable for teleparallel gravity is developed. The proposed perturbation scheme takes into account perturbations of the coframe, the metric, and the spin-connection, while ensuring that the resulting perturbed system continues to describe a teleparallel gravity situation. The resulting perturbation scheme can be transformed to one in which perturbations all take place within the co-frame. A covariant definition of a teleparallel Minkowski geometry is proposed. We compute the perturbed field equations for f(T) teleparallel gravity and discuss the stability of the teleparallel Minkowski geometry within f(T) teleparallel gravity. Full article
(This article belongs to the Special Issue Mathematical Cosmology)
12 pages, 312 KB  
Article
Stability Properties of Self-Similar Solutions in Symmetric Teleparallel f(Q)-Cosmology
by Andronikos Paliathanasis
Symmetry 2023, 15(2), 529; https://doi.org/10.3390/sym15020529 - 16 Feb 2023
Cited by 9 | Viewed by 1994
Abstract
Self-similar cosmological solutions correspond to spacetimes that admit a homothetic symmetry. The physical properties of self-similar solutions can describe important eras of the cosmological evolution. Recently, self-similar cosmological solutions were derived for symmetric teleparallel fQ-theory with different types of connections. In [...] Read more.
Self-similar cosmological solutions correspond to spacetimes that admit a homothetic symmetry. The physical properties of self-similar solutions can describe important eras of the cosmological evolution. Recently, self-similar cosmological solutions were derived for symmetric teleparallel fQ-theory with different types of connections. In this work, we study the stability properties of the self-similar cosmological solutions in order to investigate the effects of the different connections on the stability properties of the cosmic history. For the background geometry, we consider the isotropic Friedmann–Lemaître–Robertson–Walker space and the anisotropic and homogeneous Bianchi I space, for which we investigate the stability properties of Kasner-like universes. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Gravity Research)
14 pages, 301 KB  
Article
Classical and Quantum Cosmological Solutions in Teleparallel Dark Energy with Anisotropic Background Geometry
by Andronikos Paliathanasis
Symmetry 2022, 14(10), 1974; https://doi.org/10.3390/sym14101974 - 21 Sep 2022
Cited by 8 | Viewed by 1337
Abstract
We investigate exact and analytic solutions for the field equations in the teleparallel dark energy model, where the physical space is described by the locally rotational symmetric Bianchi I, Bianchi III and Kantowski-Sachs geometries. We make use of the property that a point-like [...] Read more.
We investigate exact and analytic solutions for the field equations in the teleparallel dark energy model, where the physical space is described by the locally rotational symmetric Bianchi I, Bianchi III and Kantowski-Sachs geometries. We make use of the property that a point-like Lagrangian exists for the description of the field equations, and variational symmetries are applied for the construction of invariant functions and conservation laws. The latter are used for the derivation of new analytic solutions for the classical field equations and exact function forms for the wavefunction in the quantum limit. Full article
(This article belongs to the Special Issue Exact Solutions in Modern Cosmology with Symmetry/Asymmetry)
22 pages, 1520 KB  
Article
Wormhole Solutions in Symmetric Teleparallel Gravity with Noncommutative Geometry
by Zinnat Hassan, Ghulam Mustafa and Pradyumn Kumar Sahoo
Symmetry 2021, 13(7), 1260; https://doi.org/10.3390/sym13071260 - 14 Jul 2021
Cited by 53 | Viewed by 3545
Abstract
This article describes the study of wormhole solutions in f(Q) gravity with noncommutative geometry. Here, we considered two different f(Q) models—a linear model f(Q)=αQ and an exponential model [...] Read more.
This article describes the study of wormhole solutions in f(Q) gravity with noncommutative geometry. Here, we considered two different f(Q) models—a linear model f(Q)=αQ and an exponential model f(Q)=Qα1eQ, where Q is the non-metricity and α is the model parameter. In addition, we discussed the existence of wormhole solutions with the help of the Gaussian and Lorentzian distributions of these linear and exponential models. We investigated the feasible solutions and graphically analyzed the different properties of these models by taking appropriate values for the parameter. Moreover, we used the Tolman–Oppenheimer–Volkov (TOV) equation to check the stability of the wormhole solutions that we obtained. Hence, we found that the wormhole solutions obtained with our models are physically capable and stable. Full article
(This article belongs to the Special Issue Quantum Gravity Condensates)
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19 pages, 394 KB  
Article
Static Spherically Symmetric Black Holes in Weak f(T)-Gravity
by Christian Pfeifer and Sebastian Schuster
Universe 2021, 7(5), 153; https://doi.org/10.3390/universe7050153 - 17 May 2021
Cited by 41 | Viewed by 3149
Abstract
With the advent of gravitational wave astronomy and first pictures of the “shadow” of the central black hole of our milky way, theoretical analyses of black holes (and compact objects mimicking them sufficiently closely) have become more important than ever. The near future [...] Read more.
With the advent of gravitational wave astronomy and first pictures of the “shadow” of the central black hole of our milky way, theoretical analyses of black holes (and compact objects mimicking them sufficiently closely) have become more important than ever. The near future promises more and more detailed information about the observable black holes and black hole candidates. This information could lead to important advances on constraints on or evidence for modifications of general relativity. More precisely, we are studying the influence of weak teleparallel perturbations on general relativistic vacuum spacetime geometries in spherical symmetry. We find the most general family of spherically symmetric, static vacuum solutions of the theory, which are candidates for describing teleparallel black holes which emerge as perturbations to the Schwarzschild black hole. We compare our findings to results on black hole or static, spherically symmetric solutions in teleparallel gravity discussed in the literature, by comparing the predictions for classical observables such as the photon sphere, the perihelion shift, the light deflection, and the Shapiro delay. On the basis of these observables, we demonstrate that among the solutions we found, there exist spacetime geometries that lead to much weaker bounds on teleparallel gravity than those found earlier. Finally, we move on to a discussion of how the teleparallel perturbations influence the Hawking evaporation in these spacetimes. Full article
(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)
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31 pages, 463 KB  
Review
Fundamental Symmetries and Spacetime Geometries in Gauge Theories of Gravity—Prospects for Unified Field Theories
by Francisco Cabral, Francisco S. N. Lobo and Diego Rubiera-Garcia
Universe 2020, 6(12), 238; https://doi.org/10.3390/universe6120238 - 11 Dec 2020
Cited by 36 | Viewed by 3846
Abstract
Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime geometries, providing the adequate formalism for metric-affine theories of gravity with curvature, [...] Read more.
Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime geometries, providing the adequate formalism for metric-affine theories of gravity with curvature, torsion and non-metricity. In this paper, we analyze the structure of gauge theories of gravity and consider the relation between fundamental geometrical objects and symmetry principles as well as different spacetime paradigms. Special attention is given to Poincaré gauge theories of gravity, their field equations and Noether conserved currents, which are the sources of gravity. We then discuss several topics of the gauge approach to gravitational phenomena, namely, quadratic Poincaré gauge models, the Einstein-Cartan-Sciama-Kibble theory, the teleparallel equivalent of general relativity, quadratic metric-affine Lagrangians, non-Lorentzian connections, and the breaking of Lorentz invariance in the presence of non-metricity. We also highlight the probing of post-Riemannian geometries with test matter. Finally, we briefly discuss some perspectives regarding the role of both geometrical methods and symmetry principles towards unified field theories and a new spacetime paradigm, motivated from the gauge approach to gravity. Full article
13 pages, 338 KB  
Article
Flat Connection for Rotating Vacuum Spacetimes in Extended Teleparallel Gravity Theories
by Laur Järv, Manuel Hohmann, Martin Krššák and Christian Pfeifer
Universe 2019, 5(6), 142; https://doi.org/10.3390/universe5060142 - 10 Jun 2019
Cited by 24 | Viewed by 2854
Abstract
Teleparallel geometry utilizes Weitzenböck connection which has nontrivial torsion but no curvature and does not directly follow from the metric like Levi–Civita connection. In extended teleparallel theories, for instance in f ( T ) or scalar-torsion gravity, the connection must obey its antisymmetric [...] Read more.
Teleparallel geometry utilizes Weitzenböck connection which has nontrivial torsion but no curvature and does not directly follow from the metric like Levi–Civita connection. In extended teleparallel theories, for instance in f ( T ) or scalar-torsion gravity, the connection must obey its antisymmetric field equations. Thus far, only a few analytic solutions were known. In this note, we solve the f ( T , ϕ ) gravity antisymmetric vacuum field equations for a generic rotating tetrad ansatz in Weyl canonical coordinates, and find the corresponding spin connection coefficients. By a coordinate transformation, we present the solution also in Boyer–Lindquist coordinates, often used to study rotating solutions in general relativity. The result hints for the existence of another branch of rotating solutions besides the Kerr family in extended teleparallel gravities. Full article
(This article belongs to the Special Issue Selected Papers from Teleparallel Universes in Salamanca)
34 pages, 459 KB  
Article
Scale Transformations in Metric-Affine Geometry
by Damianos Iosifidis and Tomi Koivisto
Universe 2019, 5(3), 82; https://doi.org/10.3390/universe5030082 - 15 Mar 2019
Cited by 89 | Viewed by 4169
Abstract
This article presents an exhaustive classification of metric-affine theories according to their scale symmetries. First it is clarified that there are three relevant definitions of a scale transformation. These correspond to a projective transformation of the connection, a rescaling of the orthonormal frame, [...] Read more.
This article presents an exhaustive classification of metric-affine theories according to their scale symmetries. First it is clarified that there are three relevant definitions of a scale transformation. These correspond to a projective transformation of the connection, a rescaling of the orthonormal frame, and a combination of the two. The most general second order quadratic metric-affine action, including the parity-violating terms, is constructed in each of the three cases. The results can be straightforwardly generalised by including higher derivatives, and implemented in the general metric-affine, teleparallel, and symmetric teleparallel geometries. Full article
(This article belongs to the Special Issue Selected Papers from Teleparallel Universes in Salamanca)
18 pages, 228 KB  
Article
Unification of Quantum and Gravity by Non Classical Information Entropy Space
by Germano Resconi, Ignazio Licata and Davide Fiscaletti
Entropy 2013, 15(9), 3602-3619; https://doi.org/10.3390/e15093602 - 4 Sep 2013
Cited by 19 | Viewed by 7467
Abstract
A quantum entropy space is suggested as the fundamental arena describing the quantum effects. In the quantum regime the entropy is expressed as the superposition of many different Boltzmann entropies that span the space of the entropies before any measure. When a measure [...] Read more.
A quantum entropy space is suggested as the fundamental arena describing the quantum effects. In the quantum regime the entropy is expressed as the superposition of many different Boltzmann entropies that span the space of the entropies before any measure. When a measure is performed the quantum entropy collapses to one component. A suggestive reading of the relational interpretation of quantum mechanics and of Bohm’s quantum potential in terms of the quantum entropy are provided. The space associated with the quantum entropy determines a distortion in the classical space of position, which appears as a Weyl-like gauge potential connected with Fisher information. This Weyl-like gauge potential produces a deformation of the moments which changes the classical action in such a way that Bohm’s quantum potential emerges as consequence of the non classical definition of entropy, in a non-Euclidean information space under the constraint of a minimum condition of Fisher information (Fisher Bohm- entropy). Finally, the possible quantum relativistic extensions of the theory and the connections with the problem of quantum gravity are investigated. The non classical thermodynamic approach to quantum phenomena changes the geometry of the particle phase space. In the light of the representation of gravity in ordinary phase space by torsion in the flat space (Teleparallel gravity), the change of geometry in the phase space introduces quantum phenomena in a natural way. This gives a new force to F. Shojai’s and A. Shojai’s theory where the geometry of space-time is highly coupled with a quantum potential whose origin is not the Schrödinger equation but the non classical entropy of a system of many particles that together change the geometry of the phase space of the positions (entanglement). In this way the non classical thermodynamic changes the classical geodetic as a consequence of the quantum phenomena and quantum and gravity are unified. Quantum affects geometry of multidimensional phase space and gravity changes in any point the torsion in the ordinary four-dimensional Lorenz space-time metric. Full article
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