Modified Teleparallel Gravity Research Articles

A class of static spherically symmetric solutions in f(T)-gravity

We study a class of static spherically symmetric vacuum solutions in modified teleparallel gravity solving the field equations for a specific model Ansatz, requiring the torsion scalar T to be constant. We discuss the models falling in this class. After some general considerations, we provide and investigate local solutions in the form of black holes and traversable wormholes as well as configurations that can match the anomalous rotation curves of galaxies.

Quantum cosmology in teleparallel gravity with a boundary term

We quantize a homogeneous and isotropic universe for two models of modified teleparallel gravity: one wherein an arbitrary function of the boundary term, namely B, is present in the action, and in the other model, a scalar field that is non-minimally coupled to both the torsion and boundary term. In this regard, we study exact solutions of both the classical and quantum frameworks by utilizing the corresponding Wheeler–DeWitt (WDW) equations of the models. To correspond to the comprehensive classical and quantum levels, in the second model, we propose an appropriate initial condition for the wave packets and observe that they closely adhere to the classical trajectories and reach their peak. We quantify this correspondence using the de Broglie–Bohm interpretation of quantum mechanics. According to this proposal, the classical and Bohmian trajectories coincide when the quantum potential vanishes along the Bohmian paths. Furthermore, we apply the de-parameterization technique to our model in the realm of the problem of time in quantum cosmological models based on the WDW equation, utilizing the global internal time denoted as χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi $$\\end{document}, which represents a scalar field.

Energy density inhomogeneities with self-gravitating charged fluid in modified teleparallel gravity

In this paper, we analyze energy density inhomogeneities for charged fluid configuration in the background of [Formula: see text] theory and recognize its prime features as computed in GR. The dynamical equations are composed employing Bianchi identities for the standard, [Formula: see text] extra terms, and energy-momentum tensor for the electromagnetic field. We evaluate various mathematical models of dissipative and anisotropic fluid distributions in-plane symmetry under [Formula: see text] gravity. To proceed with the investigation, we design the [Formula: see text] field equations, kinematical quantities, and mass function. We analyzed dynamical variables and Ellis equations in terms of our considered theory. To examine the associated inhomogeneity factors, specific scenarios are illustrated alongside and without dissipation. Within a non-radiating situation, we analyze dust and isotropic and anisotropic matter in the state of electric charge. We examine the inhomogeneity factor of a dissipative fluid via a charged dust haze. We derive that the electromagnetic field fosters matter inhomogeneity, but additional curvature factors make the entire structure more homogenous as time passes.

Scalar-multi-tensor approach to fT,B,∇μT,∇μB teleparallel gravity

In this work we analyze, in the context of modified teleparallel gravity, the equivalence between scalar-vector-tensor theories and geometrical theories of the type fT,B,∇μT,∇μB , where T and B are respectively the scalar torsion and the boundary scalar. This analysis is performed in the Jordan and Einstein frames. In particular, in the latter frame, two distinct cases are analyzed, where the role of surface terms is discussed. The equivalence between the geometrical and the scalar-vector-tensor approaches is verified for regular systems, i.e. for systems that present a regular Hessian matrix. An example is presented and the analysis of the Cauchy problem is made for the different approaches. An extension for systems that include higher-order derivatives of T and B is briefly presented, showing the equivalence between the geometrical and scalar-multi tensor theories.

Dark matter effects in modified teleparallel gravity

Dark matter effects in modified teleparallel gravity

Analysis of complexity on the anisotropic charged fluid in modified teleparallel gravity

This article is about the impact of complexity on the anisotropic charged fluid in f(T) gravity, where accountability of the torsion scalar T is offered by the gravitational influence. Our focus is on the anisotropic charged fluid. We took into account the static spherical distribution for the interior region. Foremost, we present the basic formalism of f(T) theory, which comprises the electric charge, and then evaluate the field equations along with the hydrostatic equilibrium equation in this framework. The criterion of complexity is taken up from Herrera’s design (Herrera, 2018), where the complexity factor is attained from the division of the Riemann curvature tensor in an orthogonal direction. We set up the relation between the Misner–Sharp mass function and the hydrostatic equilibrium equation comprising the electric charge in f(T) theory. We match the interior region with the Reissner-Nordström geometry in the exterior direction and investigate the role of the Tolman mass in this background. We carry out the analysis of the structure scalars for charged anisotropic fluid within f(T) gravity and study the impact of the density homogeneity and inhomogeneity along with local anisotropy on the complexity factor YTF. The manuscript concluded with the defined concepts that satisfy the constraint of diminishing complexity in f(T) theory, which comprises the electric charge.

Physically viable strange quark star models in modified teleparallel gravity

The aim of this paper is to develop the isotropic and anisotropic quark stars configurations in the context of [Formula: see text] gravity in the static spherically symmetric background. To explore the combined effects of torsion scalar [Formula: see text] and the trace of energy–momentum tensor (EMT) [Formula: see text] on relativistic astrophysics, we use diagonal as well as non-diagonal tetrad fields. By considering the conformal Killing vectors along with the MIT bag model, the interior solutions of the field equations corresponding to the linear [Formula: see text] model (in which [Formula: see text] are the constants and [Formula: see text] indicates the cosmological constant) are calculated. The feasibility of the obtained solutions is confirmed by implementing several physical tests. The model parameters are constrained subject to the existence and stability of the quark star models. We formulate the energy constraints, stability equations, mass function, compactness and redshift factor, and present the graphical analysis of all physical quantities. It is found that the derived solutions for both diagonal and non-diagonal tetrad exhibit well-behaved profiles in the framework of modified teleparallel gravity.

Structural properties of a new class of stellar structures in modified teleparallel gravity

This paper explores new neutron star models based on spherically symmetric space–time. We take into account the gravitational effects of f(T,T) gravity, in which T is the torsion and T is the trace of the energy–momentum tensor. Field equations are evaluated by incorporating the off-diagonal tetrad. In this paper, we discuss the detailed properties of compact star candidates 4U1538–52, J0437–4,715, J0030 + 0451, and 4U1820–30, like energy density, pressure profiles, gradients, anisotropy, energy conditions, equation of state, speeds of sound, TOV equation, and compactification parameters. We discuss all these characteristics using the quadratic cosmological model of f(T,T) gravity. We use the well-famed junction equations to evaluate the unknown parameters. Our detailed and comprehensive graphical analysis ensures that the model containing the anisotropic nature of stellar structures is physically acceptable, regular, and stable.

Quintessence anisotropic stellar models in quadratic and Born–Infeld modified teleparallel Rastall gravity

This study aims to discuss anisotropic solutions that are spherically symmetric in the quintessence field, which describe compact stellar objects in the modified Rastall teleparallel theory of gravity. To achieve this goal, the Krori and Barua arrangement for spherically symmetric components of the line element is incorporated. We explore the field equations by selecting appropriate off-diagonal tetrad fields. Born–Infeld function of torsion f(T)=βλT+1−1 and power law form h(T) = δTn are used. The Born–Infeld gravity was the first modified teleparallel gravity to discuss inflation. We use the linear equation of state pr = ξρ to separate the quintessence density. After obtaining the field equations, we investigate different physical parameters that demonstrate the stability and physical acceptability of the stellar models. We use observational data, such as the mass and radius of the compact star candidates PSRJ 1416-2230, Cen X-3, & 4U 1820-30, to ensure the physical plausibility of our findings.

Conformal motions of static cylindrically symmetric solutions in f(T, B) gravity

In this paper, we investigate the conformal vector fields (CVFs) of static cylindrically symmetric (SCS) spacetimes in [Formula: see text] gravity, a novel modified teleparallel gravity that connects both [Formula: see text] and [Formula: see text] theories via a boundary term [Formula: see text]. Initially, we employ an algebraic approach to extract some classes that represent SCS solutions in [Formula: see text] gravity. Applying the above-mentioned approach, we find solutions in nine cases. We also investigate the CVFs using the direct integration technique. Following a thorough investigation, we discover that the spacetimes admit proper CVFs in only one case. In rest of the eight cases, the spacetimes either become conformally flat or they admit homothetic vector fields (HVFs) or Killing vector fields (KVFs). The overall dimension of CVFs for the spacetimes under consideration has come out to be 5, 6 or 15. To complete the study, we also compute the energy density and pressure of each model. Corresponding to the resulting models, we discuss the energy conditions in order to check the physical sound of the solutions.

Fermion localization mechanisms in f(T,𝒯 )-brane

In this work, we investigate two mechanisms for locating fermions on the brane in a modified teleparallel gravity [Formula: see text], where [Formula: see text] is the torsion scalar and [Formula: see text] is the trace of the energy–momentum tensor. The first mechanism is a Yukawa-type minimal coupling between the fermion and the background scalar field. The second mechanism is a nonminimal coupling between the fermion and the torsion. The geometric coupling presents a greater sensitivity to the influence of torsion and to the trace of the energy–momentum tensor.

The geometrical meaning of the Weitzenböck connection

In the literature, there are many discussions about the local Lorentz invariance of modified teleparallel gravity. This symmetry is obviously violated in the classical “pure tetrad” formulation of the theory, while it gets restored in the “fully covariant” approach. My claim is that, despite many heated discussions, the two formulations are just equivalent. The purpose of this note is to argue that the local Lorentz invariance is not natural for the modified teleparallel theories at all, making the pure tetrad approach more fundamentally justified.

The effective field theory approach to the strong coupling issue in f(T) gravity

We investigate the scalar perturbations and the possible strong coupling issues of f(T) around a cosmological background, applying the effective field theory (EFT) approach. We revisit the generalized EFT framework of modified teleparallel gravity, and apply it by considering both linear and second-order perturbations for f(T) theory. We find that no new scalar mode is present in both linear and second-order perturbations in f(T) gravity, which suggests a strong coupling problem. However, based on the ratio of cubic to quadratic Lagrangians, we provide a simple estimation of the strong coupling scale, a result which shows that the strong coupling problem can be avoided at least for some modes. In conclusion, perturbation behaviors that at first appear problematic may not inevitably lead to a strong coupling problem, as long as the relevant scale is comparable with the cutoff scale M of the applicability of the theory.

A structural analysis of self-gravitating anisotropic stars via equation of state in modified teleparallel gravity

This work aims to explore spherically symmetric anisotropic solutions describing compact stellar objects in the extended teleparallel theory of gravity with matter coupling. For this purpose, we use the Adler Finch Skea geometry for both the off-diagonal and diagonal tetrads. We explore the complete matching of the tetrad fields for two different choices of the function f(T,T), i.e., linear and nonlinear models. We obtain complete solutions to the stellar models by taking the strange quark matter distribution after defining the MIT bag model equation of state, pr=13(ρ−4BG). By using the proper choice of the tetrad forms, we incorporate the generic model f(T,T)=αTn(r)+βT(r), which can be treated as linear and nonlinear models depending upon the value of parameter n. After obtaining the field equations, we investigate different physical parameters showing the stability and physical acceptability of the stellar models by using the observational data like mass and radius of PSRJ1416−2230, 4U1608−52, CenX−3, EXO1785−248, and SMCX−1 models.

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.

Localization of abelian gauge fields with Stueckelberg-like geometrical coupling on f(T, B)-thick brane

In the context of f(T, B) modified teleparallel gravity, we investigate the influence of torsion scalar T and boundary term B on the confinement of both the gauge vector and Kalb–Ramond fields. Both fields require a suitable coupling in five-dimensional braneworld scenarios to yield a normalizable zero mode. We propose a Stueckelberg-like geometrical coupling that non-minimally couples the fields to the torsion scalar and boundary term. To set up our braneworld models, we use the first-order formalism in which two kinds of superpotential are taken: sine-Gordon and phi ^{4}-deformed. The geometrical coupling is used to produce a localized zero mode. Moreover, we analyze the massive spectrum for both fields and obtain possible resonant massive modes. Furthermore, we do not find tachyonic modes leading to a consistent thick brane.

Irregular universe in the Nieh-Yan modified teleparallel gravity

The Nieh-Yan modified teleparallel gravity is a model which modifies the general relativity equivalent teleparallel gravity by a coupling between the Nieh-Yan density and an axion-like field. This model predicts parity violations in the gravitational waves if the axion-like field has a non-trivial background, and more importantly it is ghost free and avoids the pathologies presented in other parity-violating gravity models. The cosmological dynamics and perturbations of the Nieh-Yan modified teleparallel gravity have been investigated in detail, but all these previous investigations rely on the symmetry requirement that in the background universe both the metric and affine connection are homogeneous and isotropic. In this paper we relax the symmetry constraint on the connection and leave it arbitrary at the beginning, after all the cosmological principle only needs the metric of the background spacetime to meet the symmetry requirement. We find a new flat universe solution for the Nieh-Yan modified teleparallel gravity, for which the background dynamics itself is unchanged but the perturbations around it present a new feature that the scalar and tensor perturbations are coupled together at the linear level. The implications of this peculiar feature in primordial perturbations from inflation are also discussed.

Structural properties of anisotropic stars in modified teleparallel gravity: a brief study via an embedding approach

In this paper, we attempt to construct the anisotropic solution for compact stellar configurations using the observed mass and radius of compact stars from the literature under the influence of Rastall Teleparallel gravity. To investigate the crucial elements of spherically symmetric metric space, we employed the embedding class one spacetime paradigm with Karmarkar’s condition. The field equations have been computed under the gravitational action of Rastall Teleparallel gravity. However, the unknown constants were evaluated via junction conditions using the Schwarzschild metric as the outer geometry. The compact stars analysis’s crucial physical and mathematical requirements are all admitted and shared by the model, which is physically viable and supports the emergence of novel realistic stellar configurations in Rastall Teleparallel gravity. We fix the parameters of our model to compare with three compact stars (LMC X-4, Cen X-3, and EXO 1785-248) and find that it can be regular, robust, and stable.

Neutron stars in modified teleparallel gravity

We investigate compact objects in modified teleparallel gravity with realistic equations of state. We propose a modification of Teleparallel Equivalent to General Relativity, then an appropriate tetrad is applied to the field equations. A specific set of relations showing an equivalency between our gravitational model and the New General Relativity is found. The conservation equation implies that our Tolman-Oppenheimer-Volkoff equations are presented with an effective gravitational coupling constant. Numerical analysis using realistic equations of state is made, and the behavior of mass, radius, and the relation mass-radius as functions of a free parameter of our model is also investigated.

Imprints of dark matter on wormhole geometry in modified teleparallel gravity

Imprints of dark matter on wormhole geometry in modified teleparallel gravity