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3 pages, 170 KiB

Open AccessEditorial

Teleparallel Gravity: Foundations and Observational Constraints—Editorial

by Sebastian Bahamonde and Jackson Levi Said

Universe 2021, 7(8), 269; https://doi.org/10.3390/universe7080269 - 27 Jul 2021

Cited by 5 | Viewed by 1621

Abstract

Einstein’s formulation of general relativity as a theory based on the geometry of curvature was a necessity due to Riemannian geometry being the only fully developed framework at the time [...] Full article

(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)

Research

Jump to: Editorial

24 pages, 442 KiB

Open AccessArticle

Gravitationally Induced Particle Production through a Nonminimal Torsion–Matter Coupling

by Tiberiu Harko, Francisco S. N. Lobo and Emmanuel N. Saridakis

Universe 2021, 7(7), 227; https://doi.org/10.3390/universe7070227 - 5 Jul 2021

Cited by 19 | Viewed by 1947

Abstract

We investigate the possibility of gravitationally generated particle production via the mechanism of nonminimal torsion–matter coupling. An intriguing feature of this theory is that the divergence of the matter energy–momentum tensor does not vanish identically. We explore the physical and cosmological implications of [...] Read more.

We investigate the possibility of gravitationally generated particle production via the mechanism of nonminimal torsion–matter coupling. An intriguing feature of this theory is that the divergence of the matter energy–momentum tensor does not vanish identically. We explore the physical and cosmological implications of the nonconservation of the energy–momentum tensor by using the formalism of irreversible thermodynamics of open systems in the presence of matter creation/annihilation. The particle creation rates, pressure, and the expression of the comoving entropy are obtained in a covariant formulation and discussed in detail. Applied together with the gravitational field equations, the thermodynamics of open systems lead to a generalization of the standard

Λ

CDM cosmological paradigm, in which the particle creation rates and pressures are effectively considered as components of the cosmological fluid energy–momentum tensor. We consider specific models, and we show that cosmology with a torsion–matter coupling can almost perfectly reproduce the

Λ

CDM scenario, while it additionally gives rise to particle creation rates, creation pressures, and entropy generation through gravitational matter production in both low and high redshift limits. Full article

(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)

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21 pages, 1809 KiB

Open AccessArticle

Global Portraits of Nonminimal Teleparallel Inflation

by Laur Järv and Joosep Lember

Universe 2021, 7(6), 179; https://doi.org/10.3390/universe7060179 - 3 Jun 2021

Cited by 13 | Viewed by 2000

Abstract

We construct global phase portraits of inflationary dynamics in teleparallel gravity models with a scalar field nonminimally coupled to torsion scalar. The adopted set of variables can clearly distinguish between different asymptotic states as fixed points, including the kinetic and inflationary regimes. The [...] Read more.

We construct global phase portraits of inflationary dynamics in teleparallel gravity models with a scalar field nonminimally coupled to torsion scalar. The adopted set of variables can clearly distinguish between different asymptotic states as fixed points, including the kinetic and inflationary regimes. The key role in the description of inflation is played by the heteroclinic orbits that run from the asymptotic saddle points to the late time attractor point and are approximated by nonminimal slow roll conditions. To seek the asymptotic fixed points, we outline a heuristic method in terms of the “effective potential” and “effective mass”, which can be applied for any nonminimally coupled theories. As particular examples, we study positive quadratic nonminimal couplings with quadratic and quartic potentials and note how the portraits differ qualitatively from the known scalar-curvature counterparts. For quadratic models, inflation can only occur at small nonminimal coupling to torsion, as for larger coupling, the asymptotic de Sitter saddle point disappears from the physical phase space. Teleparallel models with quartic potentials are not viable for inflation at all, since for small nonminimal coupling, the asymptotic saddle point exhibits weaker than exponential expansion, and for larger coupling, it also disappears. Full article

(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)

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19 pages, 394 KiB

Open AccessArticle

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 31 | Viewed by 2470

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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13 pages, 279 KiB

Open AccessArticle

Minisuperspace Quantization of f(T, B) Cosmology

by Andronikos Paliathanasis

Universe 2021, 7(5), 150; https://doi.org/10.3390/universe7050150 - 16 May 2021

Cited by 13 | Viewed by 2113

Abstract

We discuss the quantization in the minisuperspace for the generalized fourth-order teleparallel cosmological theory known as

f (T, B)

. Specifically we focus on the case where the theory is linear on the torsion scalar, in that consideration we are able [...] Read more.

We discuss the quantization in the minisuperspace for the generalized fourth-order teleparallel cosmological theory known as

f (T, B)

. Specifically we focus on the case where the theory is linear on the torsion scalar, in that consideration we are able to write the cosmological field equations with the use of a scalar field different from the scalar tensor theories, but with the same dynamical constraints as that of scalar tensor theories. We use the minisuperspace description to write for the first time the Wheeler-DeWitt equation. With the use of the theory of similarity transformations we are able to find exact solutions for the Wheeler-DeWitt equations as also to investigate the classical and semiclassical limit in the de Broglie -Bohm representation of quantum mechanics. Full article

(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)

17 pages, 303 KiB

Open AccessArticle

Renormalizability of Alternative Theories of Gravity: Differences between Power Counting and Entropy Argument

by Francesco Bajardi, Francesco Bascone and Salvatore Capozziello

Universe 2021, 7(5), 148; https://doi.org/10.3390/universe7050148 - 14 May 2021

Cited by 10 | Viewed by 2116

Abstract

It is well known that General Relativity cannot be considered under the standard of a perturbatively renormalizable quantum field theory, but asymptotic safety is taken into account as a possibility for the formulation of gravity as a non-perturbative renormalizable theory. Recently, the entropy [...] Read more.

It is well known that General Relativity cannot be considered under the standard of a perturbatively renormalizable quantum field theory, but asymptotic safety is taken into account as a possibility for the formulation of gravity as a non-perturbative renormalizable theory. Recently, the entropy argument has however stepped into the discussion claiming for a “no-go” to the asymptotic safety argument. In this paper, we present simple counter-examples, considering alternative theories of gravity, to the entropy argument as further indications, among others, on the possible flows in the assumptions on which the latter is based. We considered different theories, namely curvature-based extensions of General Relativity as

f (R)

,

f (G)

, extensions of teleparallel gravity as

f (T)

, and Horava–Lifshitz gravity, working out the explicit spherically symmetric solutions in order to make a comparison between power counting and the entropy argument. Even in these cases, inconsistencies were found. Full article

(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)

16 pages, 301 KiB

Open AccessArticle

Accidental Gauge Symmetries of Minkowski Spacetime in Teleparallel Theories

by Jose Beltrán Jiménez and Tomi S. Koivisto

Universe 2021, 7(5), 143; https://doi.org/10.3390/universe7050143 - 12 May 2021

Cited by 27 | Viewed by 1738

Abstract

In this paper, we provide a general framework for the construction of the Einstein frame within non-linear extensions of the teleparallel equivalents of General Relativity. These include the metric teleparallel and the symmetric teleparallel, but also the general teleparallel theories. We write the [...] Read more.

In this paper, we provide a general framework for the construction of the Einstein frame within non-linear extensions of the teleparallel equivalents of General Relativity. These include the metric teleparallel and the symmetric teleparallel, but also the general teleparallel theories. We write the actions in a form where we separate the Einstein–Hilbert term, the conformal mode due to the non-linear nature of the theories (which is analogous to the extra degree of freedom in f(R) theories), and the sector that manifestly shows the dynamics arising from the breaking of local symmetries. This frame is then used to study the theories around the Minkowski background, and we show how all the non-linear extensions share the same quadratic action around Minkowski. As a matter of fact, we find that the gauge symmetries that are lost by going to the non-linear generalisations of the teleparallel General Relativity equivalents arise as accidental symmetries in the linear theory around Minkowski. Remarkably, we also find that the conformal mode can be absorbed into a Weyl rescaling of the metric at this order and, consequently, it disappears from the linear spectrum so only the usual massless spin 2 perturbation propagates. These findings unify in a common framework the known fact that no additional modes propagate on Minkowski backgrounds, and we can trace it back to the existence of accidental gauge symmetries of such a background. Full article

(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)

11 pages, 275 KiB

Open AccessCommunication

Approaches to Spherically Symmetric Solutions in f(T) Gravity

by Alexey Golovnev and María-José Guzmán

Universe 2021, 7(5), 121; https://doi.org/10.3390/universe7050121 - 29 Apr 2021

Cited by 24 | Viewed by 1515

Abstract

We study properties of static spherically symmetric solutions in

f (T)

gravity. Based on our previous work on generalizing Bianchi identities for this kind of theory, we show how this search for solutions can be reduced to the study of two [...] Read more.

We study properties of static spherically symmetric solutions in

f (T)

gravity. Based on our previous work on generalizing Bianchi identities for this kind of theory, we show how this search for solutions can be reduced to the study of two relatively simple equations. One of them does not depend on the function f and therefore describes the properties of such solutions in any

f (T)

theory. Another equation is the radial one and, if a possible solution is chosen, it allows the discovery of which function f is suitable for it. We use these equations to find exact and perturbative solutions for arbitrary and specific choices of f. Full article

(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)

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25 pages, 348 KiB

Open AccessArticle

Variational Principles in Teleparallel Gravity Theories

by Manuel Hohmann

Universe 2021, 7(5), 114; https://doi.org/10.3390/universe7050114 - 21 Apr 2021

Cited by 37 | Viewed by 3159

Abstract

We study the variational principle and derivation of the field equations for different classes of teleparallel gravity theories, using both their metric-affine and covariant tetrad formulations. These theories have in common that, in addition to the tetrad or metric, they employ a flat [...] Read more.

We study the variational principle and derivation of the field equations for different classes of teleparallel gravity theories, using both their metric-affine and covariant tetrad formulations. These theories have in common that, in addition to the tetrad or metric, they employ a flat connection as additional field variable, but dthey iffer by the presence of absence of torsion and nonmetricity for this independent connection. Besides the different underlying geometric formulation using a tetrad or metric as fundamental field variable, one has different choices to introduce the conditions of vanishing curvature, torsion, and nonmetricity, either by imposing them a priori and correspondingly restricting the variation of the action when the field equations are derived, or by using Lagrange multipliers. Special care must be taken, since these conditions form non-holonomic constraints. Here, we explicitly show that all of the aforementioned approaches are equivalent, and that the same set of field equations is obtained, independently of the choice of the geometric formulation and variation procedure. We further discuss the consequences arising from the diffeomorphism invariance of the gravitational action, and show how they establish relations between the gravitational field equations. Full article

(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)

18 pages, 466 KiB

Open AccessArticle

Perturbations of the Gravitational Energy in the TEGR: Quasinormal Modes of the Schwarzschild Black Hole

by José Wadih Maluf, Sérgio Ulhoa, Fernando Lessa Carneiro and Karlúcio H. C. Castello-Branco

Universe 2021, 7(4), 100; https://doi.org/10.3390/universe7040100 - 14 Apr 2021

Cited by 4 | Viewed by 2212

Abstract

We calculate the gravitational energy spectrum of the perturbations of a Schwarzschild black hole described by quasinormal modes, in the framework of the teleparallel equivalent of general relativity (TEGR). We obtain a general formula for the gravitational energy enclosed by a large surface [...] Read more.

We calculate the gravitational energy spectrum of the perturbations of a Schwarzschild black hole described by quasinormal modes, in the framework of the teleparallel equivalent of general relativity (TEGR). We obtain a general formula for the gravitational energy enclosed by a large surface of constant radius r, in the region

m < < r < < \infty

, where m is the mass of the black hole. Considering the usual asymptotic expression for the perturbed metric components, we arrive at finite values for the energy spectrum. The perturbed energy depends on the two integers n and l that describe the quasinormal modes. In this sense, the energy perturbations are discretized. We also obtain a simple expression for the decrease of the flux of gravitational radiation of the perturbations. Full article

(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)

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13 pages, 259 KiB

Open AccessArticle

An Improved Framework for Quantum Gravity

by José G. Pereira and Diego F. López

Universe 2020, 6(12), 243; https://doi.org/10.3390/universe6120243 - 16 Dec 2020

Cited by 3 | Viewed by 2498

Abstract

General relativity has two fundamental problems that render it unsuitable for tackling the gravitational field’s quantization. The first problem is the lack of a genuine gravitational variable representing gravitation only, inertial forces apart. The second problem is its incompatibility with quantum mechanics, a [...] Read more.

General relativity has two fundamental problems that render it unsuitable for tackling the gravitational field’s quantization. The first problem is the lack of a genuine gravitational variable representing gravitation only, inertial forces apart. The second problem is its incompatibility with quantum mechanics, a problem inherited from the more fundamental conflict of special relativity with quantum mechanics. A procedure to overcome these difficulties is outlined, which amounts to replacing general relativity with its teleparallel equivalent and the Poincaré-invariant special relativity with the de Sitter-invariant special relativity. Those replacements give rise to the de Sitter-modified teleparallel gravity, which does not have the two mentioned problems. It can thus be considered an improved alternative approach to quantum gravity. Full article

(This article belongs to the Special Issue Teleparallel Gravity: Foundations and Observational Constraints)

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