Teleparallel Theory Of Gravity Research Articles

Casimir wormhole with GUP correction in extended symmetric teleparallel gravity

Quantum mechanical concept such as the Casimir effect is explored to model traversable wormholes in an extended symmetric teleparallel gravity theory. The minimal length concept leading to the generalized uncertainty principle (GUP) is used to obtain the Casimir energy density. The effect of the GUP correction in the geometrical and physical properties of traversable Casimir wormholes are investigated. It is noted that the GUP correction has a substantial effect on the wormhole geometry and it modifies the energy condition. From a detailed calculation of the exotic matter content of the GUP corrected Casimir wormhole, it is shown that, a minimal amount of exotic matter is sufficient to support the stability of the wormhole.

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The pursuit of understanding the mysteries surrounding dark energy has sparked significant interest within the field of cosmology. While conventional approaches, such as the cosmological constant, have been extensively explored, alternative theories incorporating scalar field-based models and modified gravity have emerged as intriguing avenues. Among these, teleparallel theories of gravity, specifically the f(T,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T,\\phi )$$\\end{document} formulation, have gained prominence as a means to comprehend dark energy within the framework of teleparallelism. In this study, we investigate two well-studied models of teleparallel dark energy and examine the presence of cosmological singularities within these scenarios. Using the Goriely–Hyde procedure, we examine the dynamical systems governing the cosmological equations of these models. Our analysis reveals that both models exhibit Type IV singularities, but only for a limited range of initial conditions. These results could indicate a potential edge for teleparallel cosmological models over their other modified gravity counterparts, as the models we examine seem to be only allowing for weak singularities that too under non general conditions.

General teleparallel gravity from Finsler geometry

Riemannian geometry, as a basis for general relativity, can be obtained from the more general Finsler geometry in terms of the Cartan connection and Chern connection, as discussed frequently in the literature. However, there are other gravity theories that can be made to be equivalent to general relativity but are based on non-Riemannian geometry. Famous examples are the Teleparallel and Symmetric Teleparallel gravity theories. In this paper, we show how to obtain the geometry for Teleparallel gravity from Finsler geometry in terms of a ‘Teleparallel type’ connection.

On torsion axial vector and gravitational energy in Lewis–Papapetrou space-time in the theory of teleparallel gravity

The teleparallel version of Lewis–Papapetrou space-time is investigated. For this space-time, the true discussion of the geometric and physical properties is given. We show that the value of the space-like torsion-axial vector does not depend on the choice of tetrad field. Consequently, the spin procession of the Dirac particle and the corresponding Hamiltonian have physical meaning. The energy and momentum densities for such space-time are calculated. We show that when choosing two sets of tetrad fields, the dependence and independence of the aforementioned quantities on the tetrad field depend on the Lorentz factor, which links the two sets of tetrad fields.

Covariant spin-parity decomposition of the torsion and path integrals

We propose a functional measure over the torsion tensor. We discuss two completely equivalent choices for the Wheeler–DeWitt supermetric for this field, the first one is based on its algebraic decomposition and the other is inspired by teleparallel theories of gravity. The measure is formally defined by requiring the normalization of the Gaußian integral. To achieve such a result we split the torsion tensor into its spin-parity eigenstates by constructing a new, York-like, decomposition. Of course, such a decomposition has a wider range of applicability to any kind of tensor sharing the symmetries of the torsion. As a result of this procedure a functional Jacobian naturally arises, whose formal expression is given exactly in the phenomenologically interesting limit of maximally symmetric spaces. We also discuss the explicit computation of this Jacobian in the case of a four-dimensional sphereS 4 with particular emphasis on its logarithmic divergences.

Scalar induced gravitational waves in modified teleparallel gravity theories

Primordial black holes (PBHs) forming out of the collapse of enhanced cosmological perturbations provide access to the early Universe through their associated observational signatures. In particular, enhanced cosmological perturbations collapsing to form PBHs are responsible for the generation of a stochastic gravitational-wave background (SGWB) induced by second-order gravitational interactions, usually called scalar induced gravitational waves (SIGWs). This SGWB is sensitive to the underlying gravitational theory; hence it can be used as a novel tool to test the standard paradigm of gravity and constrain possible deviations from general relativity. In this work, we study the aforementioned GW signal within modified teleparallel gravity theories, developing a formalism for the derivation of the GW spectral abundance within any form of gravitational action. At the end, working within viable $f(T,\ensuremath{\phi})$ models without matter-gravity couplings, and accounting for the effect of monoparametric $f(T)$ gravity at the level of the source and the propagation of the tensor perturbations, we show that the respective GW signal is indistinguishable from that within GR. Interestingly, we find that in order to break the degeneracy between different $f(T)$ theories through the portal of SIGWs one should necessarily consider nonminimal matter-gravity couplings at the level of the gravitational action.

Geometrical trinity of unimodular gravity

We construct a Weyl transverse diffeomorphism invariant theory of teleparallel gravity by employing the Weyl compensator formalism. The low-energy dynamics has a single spin two gravition without a scalar degree of freedom. By construction, it is equivalent to unimodular gravity (as well as Einstein’s general relativity with an adjustable cosmological constant) at the non-linear level. Combined with our earlier construction of a Weyl transverse diffeomorphism invariant theory of symmetric teleparallel gravity, unimodular gravity is represented in three alternative ways.

General effective field theory of teleparallel gravity

We construct the effective field theory (EFT) of the teleparallel equivalent of general relativity (TEGR). Firstly, we present the necessary field redefinitions of the scalar field and the tetrads. Then we provide all the terms at next-to-leading-order, containing the torsion tensor and its derivatives, and derivatives of the scalar field, accompanied by generic scalar-field-dependent couplings, where all operators are suppressed by a scale Λ. Removing all redundant terms using the field redefinitions we result to the EFT of TEGR, which includes significantly more terms comparing to the EFT of general relativity (GR). Finally, we present an application in a cosmological framework. Interestingly enough, although GR and TEGR are completely equivalent at the level of classical equations, we find that their corresponding EFTs possess minor but non-zero differences. Hence, we do verify that at higher energies the excitation and the features of the extra degrees of freedom are slightly different in the two theories, thus making them theoretically distinguishable. Nevertheless, we mention that these differences are suppressed by the heavy mass scale Λ and thus it is not guaranteed that they could be measured in future experiments and observations.

Homogeneous and isotropic cosmology in general teleparallel gravity

We derive the most general homogeneous and isotropic teleparallel geometries, defined by a metric and a flat, affine connection. We find that there are five branches of connection solutions, which are connected via several limits, and can further be restricted to the torsion-free and metric-compatible cases. We apply our results to several classes of general teleparallel gravity theories and derive their cosmological dynamics for all five branches. Our results show that for large subclasses of these theories the dynamics reduce to that of closely related metric or symmetric teleparallel gravity theories, while for other subclasses up to two new scalar degrees of freedom participate in the cosmological dynamics.

Teleparallel geometry with a single affine symmetry

In teleparallel geometries, symmetries are represented by affine frame symmetries that constrain both the (co)frame basis and the spin-connection (which are the primary geometric objects). In this paper, we shall study teleparallel geometries with a single affine symmetry, utilizing the locally Lorentz covariant approach and adopting a complex null gauge. We first introduce an algorithm to study geometries with an affine frame symmetry, which consists of choosing coordinates adapted to the symmetry, constructing a canonical frame, and solving the equations describing the symmetry. All of the constraints on the geometry are determined in the case of a single affine symmetry, but there are additional constraints arising from the field equations for a given theory of teleparallel gravity. In particular, we find that in f(T) teleparallel gravity there will be severe constraints on the geometry arising from the antisymmetric part of the field equations.

Discrete Gravity in Emergent Space Theory: Hidden Conical Defects and Teleparallel Gravity

In the first part of the paper, we try to identify the presence of gravity, at a microscopic level, by introducing conical defects and maintaining an approach that assumes topological equivalence among the underlying manifolds that form the tissue of the D-brane itself. In the second part, we will present an alternative to the conical defects, considering the theory of teleparallel gravity, in which the presence of the torsion and the construction of the brane always occurs within the context of our new interpretation of emergent spaces.

Symmetric teleparallel geometries

In teleparallel gravity and, in particular, in F(T) teleparallel gravity, there is a challenge in determining an appropriate (co-)frame and its corresponding spin connection to describe the geometry. Very often, the ‘proper’ frame, the frame in which all inertial effects are absent, is not the simplest (e.g, diagonal) (co-)frame. The determination of the frame and its corresponding spin connection for F(T) teleparallel gravity theories when there exist affine symmetries is of much interest. In this paper we present the general form of the coframe and its corresponding spin connection for teleparallel geometries which are invariant under a G 6 group of affine symmetries. The proper coframe and the corresponding F(T) field equations are also shown for these teleparallel Robertson–Walker geometries. Further, with the addition of an additional affine symmetry, it is possible to define a teleparallel de Sitter geometry.

Gravitational wave birefringence in spatially curved teleparallel cosmology

We study tensor perturbations around the most general cosmologically symmetric backgrounds in a class of teleparallel gravity theories known as New General Relativity. These theories comprise a one-parameter class, which is fully consistent with observations at the post-Newtonian level, and which contains the teleparallel equivalent of General Relativity as a special case. We find that for a particular class of cosmological background geometries these theories exhibit gravitational wave birefringence and dispersion, i.e., the dispersion relation for gravitational waves depends on their polarization and wave number. The strength of this effect is directly related to the spatial curvature of the cosmological background and the parameter describing the deviation of the theory from General Relativity. We discuss the possibility of observing this effect in gravitational wave experiments.

Analytical stellar models of neutron stars in teleparallel gravity

In this paper, we use the theory of teleparallel gravity to develop three analytical models and obtain a new class of solutions describing compact stellar structures. We investigate the anisotropic nature of stellar configurations in general and solve teleparallel gravity equations. To thoroughly analyze the various parameters of the stars, we develop three models by choosing various physically acceptable forms of metric potential \(e^{d(r)}\) and radial pressure \(p_r(r)\). We also analyze the impact of teleparallel gravity’s parameters \(\beta\) and \(\beta _1\) on the description of the stellar structures. We calculated model parameters so that models describing various observed neutron stars obey all physical conditions necessary to be potentially stable and causal. By analyzing the impact of various parameters of teleparallel gravity on the description of anisotropic stellar structures, we show that these three models can describe anisotropic neutron stars ranging from low density to high density. Finally, we obtain a quadratic equation of state for each model describing various neutron stars, which can be utilized to find compositions of the stellar structures. It is extremely useful to find models that can exhibit quadratic EOS, because various authors have discovered that the material compositions of real neutron stars and strange stars exhibit quadratic EOS. Since a nonlinear f(T) model gives a high deviation of EOS from the quadratic behavior, we work with a linear f(T) function by using a diagonal tetrad to model realistic compact stars.

Configurational entropy and braneworlds in f(T,B) gravity

The thick brane scenario built on the [Formula: see text] teleparallel gravity theory was considered for the study of phase transitions, internal structures and new classes of solutions in a model. In this theory, [Formula: see text] denotes the torsion scalar and [Formula: see text] is a boundary term. An interesting result was observed when brane splitting occurs, i.e. internal structures in the model arise as a consequence of the appearance of new domain walls in the theory. In fact, this preliminary result influences the profile of the matter field (from kink to multikink) so that for appropriate values of the parameters [Formula: see text], multiple phase transitions are identified. To perform this analysis, the Differential Configurational Entropy (DCE) that has the ability to predict the existence of phase transitions through critical points was used. Furthermore, the DCE is able to select the most stable solutions since it gives us details about the informational content to the field settings.

A note on the equivalence of energy–momentum distribution for diagonal and non-diagonal models in general relativity and teleparallel gravity

In this paper, it is shown that the super-potential defined by Einstein, Landau–Lifshitz, and Bergmann–Thompson in general relativity theory and in teleparallel gravity theory are equivalent for a general diagonal space–time metric. Therefore, the energy–momentum tensor defined by Einstein, Landau–Lifshitz, and Bergmann–Thompson is equivalent in general relativity theory and in teleparallel gravity theory for the general diagonal space–times. Two different examples are also given to ensure the validity of the established statements. However, this fact is not true in general for the non-diagonal space–times. Non-diagonal Phantom black hole metric and non-diagonal stationary axi-symmetric space–time are introduced as a counter-examples to prove the non-equivalence of the super-potential and energy–momentum tensor defined in general relativity theory and in teleparallel gravity theory.

Weyl transverse diffeomorphism invariant theory of symmetric teleparallel gravity

We construct a Weyl transverse diffeomorphism invariant theory of symmetric teleparallel gravity by employing the Weyl compensator formalism. The low-energy dynamics has a single spin two gravitation without a scalar degree of freedom. By construction, it is equivalent to the unimodular gravity (as well as the Einstein gravity) at the non-linear level.

Parametrized post-Newtonian formalism in higher-order Teleparallel Gravity

We study the parametrized post-Newtonian (PPN) limit of higher-derivative-torsion Modified Teleparallel Gravity. We start from the covariant formulation of modified Teleparallel Gravity by restoring the spin connection of the theory. Then, we perform the post-Newtonian expansion of the tetrad field around the Minkowski background and find the perturbed field equations. We compute the PPN metric for the higher-order Teleparallel Gravity theories which allows us to show that at the post-Newtonian limit this more general class of theories are fully conservative and indistinguishable from General Relativity . In this way, we extend the results that were already found for F(T) gravity in previous works. Furthermore, our calculations reveal the importance of considering a second post-Newtonian (2PN) order approximation or a parametrized post-Newtonian cosmology (PPNC) framework where additional perturbative modes coming from general modifications of Teleparallel Gravity could lead to new observable imprints.

Tilted congruence with big rip singularity in f(T) theory of gravity

In this paper, tilted congruence with big rip singularity in f(T) theory of gravity is presented. f(T) theory of gravity is the generalization of the Teleparallel theory of gravity, where [Formula: see text] is the torsion scalar. In this work, tilted model is studied in which the three-velocity represents additional degree of freedom and tilted model detected the presence of dissipative processes including gravitational radiation. The solution of the field equations is explored by using the stiff fluid, power law of velocity field and a linear relationship between [Formula: see text] and [Formula: see text]. In this paper, the big bang and big rip singularity are observed. The cosmological evolution in f(T) model is examined. The physical and geometrical phases of the models are also investigated.

Galactic dynamo seeds and black hole singularities driven by Einstein–Cartan QCD walls

Torsion spin polarised wall solution of Einstein–Cartan equations as torsion defects (Garcia de Andrade, Ann Phys 432 (2021)) where spin is distributed orthogonally to the wall has recently been obtained. Moreover, torsional inflating defect [Class and Quantum Gravity, 16 (1999) 2097] in the form of a dilatonic domain wall has also been found. Our goal in this paper is to obtain thin torsion wall solutions as teleparallel and Riemann–Cartan (RC) spacetime walls, with Einstein–Cartan stress–energy tensor, similar to Kalb–Ramond torsion fields. In thin teleparallel wall, we show that torsion is proportional to a time Dirac delta function which possesses a time singularity at the wall like Big Bang and black hole GR ones. This magnetic field has a torsional contribution of BQCD∼1017G in RC walls, which is suitable for dynamo amplification from a seed field of Bseed∼1012G as Big Bang Nucleosynthesis (BBN). From QCD cosmic time scale of tQCD∼10−6s torsion of the order of J0∼10−11cm−1 is obtained. From a 1 MeV torsion and seed field of Bseed∼10−32G, found by Barrow et al [PRD] in the framework of general relativity (GR) which is suitable to seed galactic dynamo field. In this case a domain wall magnetic field of BDW∼10−28G which is stronger, and more suitable as a galactic dynamo seed, is obtained. Magnetic field seed of 10−14G, quite close to orders of magnitude of O(10−15−10−18G) obtained by Atrayed et al. (EPJC (2018) 78: 1027) on a torsionless GR domain wall, generates a wall (DW) magnetic field of order of BDW∼1018G obtained at 1 kpc scales. These similarities between GR results and teleparallel one were expected due to the fact that the teleparallel theory of gravity considered in this paper is the teleparallel equivalent to GR or (TEGR). Chiral dynamos in dilatonic conformally flat metric are also discussed.