Extended Teleparallel Gravity Research Articles

Structural properties of compact stars in extended Teleparallel gravity

In this study, the structures of stars are examined using the Karmarkar condition (KC) to assess the metric components. The study also takes into account the anisotropic source of the matter distribution in the context of Modified Teleparallel Rastall Gravity (MTRG). Various values of the model parameter [Formula: see text] are tested by assuming different metric coefficients for the embedding spacetime. To calculate the involved model parameters, the Schwarzschild black hole solution is employed as an exterior solution. The stability and admissibility of the solutions obtained are demonstrated by analyzing some core properties of stellar objects, using observed data from established stellar models such as “PSRJ1416-2230”. It is worth noting that the results obtained in this study are physically feasible and acceptable.

Dynamical system analysis in teleparallel gravity with boundary term

In this paper, we perform the dynamical system analysis of the cosmological models framed in the extended teleparallel gravity, the f(T, B) gravity. We use the mapping, f(T, B)rightarrow -T+tilde{f}(T, B), and define the dynamical variables to form the autonomous dynamical system. The critical points are obtained in two well-motivated forms of f(T, B), one that involves the logarithmic form of the boundary term B, and the other one is the non-linear form of the boundary term. The position of critical points is shown in the different evolutionary phases of the Universe such as radiation, matter, and de-Sitter phase. The stability condition of each of the critical points of both the models is derived and the behavior of each point has been obtained mathematically and through the phase portrait. The evolution of standard density parameters such as radiation (Omega _{r}), matter (Omega _{m}), and dark energy (Omega _{DE}) are also analyzed. Further to connect with the present cosmological scenario, the behavior of deceleration and equation of state parameter both in the dark energy phase (omega _{DE}) and total (omega _{tot}) are shown from the initial condition of the dynamical variables. The accelerating behaviour has been obtained for both models.

Production of primordial gravitational waves in teleparallel gravity

We study the production of primordial gravitational waves in the context of extended teleparallel gravity models and compare them with those of general relativity. Teleparallel gravity has been widely studied in the context of the late universe but not much in the early universe. Two sources of primordial gravitational waves are considered, vacuum fluctuations and tensor anisotropies within two inflation-compatible backgrounds: a perfect de Sitter and a quasi de Sitter background. We find that in the vacuum case with a perfect de Sitter background, the gravitational waves propagation equation is the same as that of general relativity, however, if the background is promoted to a quasi de Sitter background, the propagation equations are different resulting in an important difference on the tensor spectral index. When tensor anisotropies are included, we compute the most general solution for gravitational waves in terms of a retarded Green’s function and analyze the contributions to the power spectrum from these anisotropies. Finally, we investigate the energy density of these gravitational waves.

Relativistic Wormholes in Extended Teleparallel Gravity with Minimal Matter Coupling

AbstractThis study explores the wormhole solutions utilizing the notion of conformal symmetry in the background of the gravity. The exact shape functions are calculated using the Gaussian and Lorentzian distributions as the noncommutative source of the energy density. All the energy conditions are checked for the two different shape functions. The presence of exotic matter is confirmed due to the violation of the null energy conditions. The physical aspects of the epicyclic frequencies of test particles are discussed in the spacetime geometry of the obtained wormholes in the current analysis and it is shown that how they depend on the spacetime parameters. The red‐blue shifts for the photons emitted by the orbiting test particles are also investigated and their dependence on the spacetime parameters is discussed. Further, the stability of the developed structure of the traversable wormholes is investigated by using the Tolman‐Oppenheimer‐Volkoff equation.

Reconstruction of cosmological models in a general gravitational framework involving torsion scalar

This study is elaborated to reconstruct some cosmological models in the gravitational framework of an extended teleparallel gravity based on the higher-order derivative terms of torsion scalar. To achieve this goal, we consider spatially flat FRW model with perfect fluid as background matter distribution. In this framework, we find some interesting exact solutions by using the hybrid and intermediate forms of scale factor via a well-known reconstruction scheme. For exploring physical significance of the reconstructed solutions, we analyze the behavior of dark energy EoS parameter, the validity of energy condition bounds as well as the generalized second law of thermodynamics graphically. For investigating the stability of reconstructed solutions, we check the behavior of speed of sound [Formula: see text] in each case. It is seen that in de Sitter case, the reconstruction of full Lagrangian function is not possible as it reduces to the case of simple [Formula: see text] gravity which has already been discussed in literature. While for power law form of scale factor, it is found that reconstruction is possible and most of the obtained solutions favor the quintessence era of cosmic evolution. Further, it is concluded that both the energy conditions and generalized second thermodynamical law hold for the reconstructed solutions and these solutions exhibit stable behavior (as [Formula: see text]). Lastly, in case of intermediate form of scale factor, the resulting differential equations are very complicated and hence the analytical solution is possible only for the simplest case which, further, indicates cosmologically promising behavior.

Testing Born–Infeld f(T) teleparallel gravity through Sgr hbox {A}^star observations

We use observational data from the S2 star orbiting around the Galactic Center to constrain a black hole solution of extended teleparallel gravity models. Subsequently, we construct the shadow images of Sgr hbox {A}^{star } black hole. In particular, we constrain the parameter alpha =1/lambda which appears in the Born–Infeld f(T) model. In the strong gravity regime we find that the shadow radius increases with the increase of the parameter alpha . Specifically, from the S2 star observations, we find within 1sigma that the parameter must lie between 0 le alpha /M^2 le 6 times 10^{-4}. Consequently, we used the best fit parameters to model the shadow images of Sgr hbox {A}^{star } black hole and then using the Gauss-Bonnet theorem we analysed the deflection angle for leading order expansions of the parameter alpha . It is found that within the parameter range, these observables are very close to the Schwarzschild case. Furthermore, using the best fit parameters for the Born–Infeld f(T) model we show that the angular diameter is consistent with recent observations for the Sgr hbox {A}^{star } with angular diameter (51.8 pm 2.3) mu arcsec and difficult to be distinguished from the GR. For the deflection angle of light, in leading order terms, we find that the deflection angle expressed in the ADM mass coincides with the GR, but the ADM mass in the Born–Infeld f(T) gravity increases with the increase of alpha and the overall deflection angle is expected to me greater in f(T) gravity. As a consequence of this fact, we have shown that the electromagnetic intensity observed in shadow images is smaller compared to GR.

The amplification of cosmological magnetic fields in extended f(T,B) teleparallel gravity

Observations indicate that intergalactic magnetic fields have amplitudes of the order of ∼ 10-6 G and are uniform on scales of ∼ 10 kpc. Despite their wide presence in the Universe, their origin remains an open issue. Even by invoking a dynamo mechanism or a compression effect for magnetic field amplification, the existence of seed fields before galaxy formation is still problematic. General Relativity predicts an adiabatic decrease of the magnetic field evolving as |B| ∝ 1/a 2, where a is the scale factor of the Universe. It results in very small primordial fields, unless the conformal symmetry of the electromagnetic sector is broken. In this paper, we study the possibility that a natural mechanism for the amplification of primordial magnetic field can be related to extended teleparallel gravity f(T,B) models, where T is the torsion scalar, and B the boundary term. In particular, we consider a non-minimal coupling with gravity in view to break conformal symmetry in a teleparallel background, investigating, in particular, the role of boundary term B, which can be consider as a further scalar field. We find that, after solving exactly the f(T,B) field equations both in inflation and reheating eras, a non-adiabatic behavior of the magnetic field is always possible, and a strong amplification appears in the reheating epoch. We also compute the ratio r = ρB /ργ between the magnetic energy density and the cosmic microwave energy density during inflation, in order to explain the present value r ≃ 1, showing that, in the slow-roll approximation, power-law teleparallel theories with Bn have effects indistinguishable from metric theories Rn where R is the Ricci curvature scalar.

Study on anisotropic star in extended teleparallel gravity with minimal matter coupling

This manuscript explores the physical aspects of compact stars in f(τ,T) gravity, where τ and T express the torsion and trace of the energy–momentum tensor. To achieve this goal, we consider a spherically symmetric spacetime with an anisotropic source of fluid. In particular, the Karori–Barua spacetime is considered to explore the solution of compact stars. In addition, we select three specific types of compact stars models, namely PSRJ1416−2230, 4U1608−52, and CenX−3. We develop the field equations using the Karori–Barua spacetime with some specific form of f(τ,T) gravity. In addition, we consider the Schwarzschild geometry for the matching conditions at the boundary. Then, we calculate the values of all the relevant parameters by imposing matching conditions. We provide detailed graphical analyses for the physical acceptability of different parameters, namely energy density, pressure, anisotropy, and gradient. We also examine the stability of compact stars by exploring energy conditions, equations of state, conditions of causality, redshift functions, mass functions, and compactness functions. Finally, we find that the solutions we obtained are physically viable in modified physical acceptability and also it has good properties for the compact star models.

Noether symmetries and quantum cosmology in extended teleparallel gravity

We apply the Noether Symmetry Approach to point-like teleparallel Lagrangians in view to derive minisuperspaces suitable for Quantum Cosmology. Adopting the Arnowitt–Deser–Misner formalism, we find out related Wave Functions of the Universe. Specifically, by means of appropriate changes of variables suggested by the existence of Noether symmetries, it is possible to obtain the cosmological Hamiltonians whose solutions are classical trajectories interpretable as observable universes.

Cosmic acceleration and stability of cosmological models in extended teleparallel gravity

In this paper, we study the model of f(T) gravity in the presence of dark matter and modified holographic Ricci dark energy (MHRDE) in locally rotationally symmetric (LRS) Bianchi type-I space–time. To achieve a physically realistic solution of the field equations, we have considered volumetric power and exponential expansion laws. We plot the corresponding cosmological parameters for dark energy components in terms of redshift; thereafter we investigate the accelerated expansion of the Universe. The physical and geometrical parameters of the models are also discussed in detail. The Statefinder diagnostic pair and jerk parameter are analysed to characterise completely different phases of the Universe.

Focusing conditions for extended teleparallel gravity theories

In the context of extended theories of teleparallel gravity f(T) we derive the focusing conditions for a one-parameter dependent congruence of timelike auto-parallels of the Levi-Civita connection. We also consider the f(T) field equations for a general metric tensor before moving on to consider a spatially flat Robertson-Walker space-time. Following this, we study the expansion rate for a one-parameter dependent congruence of timelike auto-parallel curves of the Levi-Civita connection. Given the fact that test particles follow auto-parallels of the Levi-Civita connection, the torsion-free Raychaudhuri equation is used in order to determine the desired focusing conditions. Finally we study the obtained focusing conditions for three f(T) paradigmatic cosmological models and discuss the satisfaction or violation of these conditions. Through this, we find f(T) models that allow for the weak and strong focusing conditions to be satisfied or violated. It is mentioned that this behaviour can also be found in the so-called f(R) and f(Q) theories.

A study of anisotropic spheres in modified gravity via embedding approach

The motivation of this paper is based on the foundation of extended teleparallel gravity with matter coupling to prospect the accelerated expansion of the Universe. This theory based on the torsion scalar along with the trace term of energy stress tensor. We manipulate the spherical symmetric metric and anisotropic fluid to discuss the study of stellar structures. To interpret our research, we used the observational data of three stars. We adopt the process of parallelism of interior and exterior space-times to estimate the unspecified parameters used in the stellar discussion. Further, we discuss the stellar properties like energy density, progressive behavior of radial and tangential components of pressure, the anisotropic formation of the compact stars. We also analyze the physical presence of stars by discussing the energy conditions redshift and mass functions. We signify the stability of the system by examining the speed of sounds and EoS. We show the equilibrium of the system by analyzing the TOV equation. Finally, we show that our system in the discussion is physically stable and analytically viable.

Lorentz distributed wormhole solutions in f(T) gravity with off-diagonal tetrad under conformal motions

In this work, the possible existence of wormhole solutions have been investigated in the extended teleparallel [Formula: see text] theory of gravity by incorporating the Lorentzian source of non-commutative geometry through the conformal motion. The physical concept of conformal symmetry becomes more arguable when it is discussed in the background of non-commutative geometry, especially with the Lorentzian source. In this context, two specific different models of the extended teleparallel theory, that is, [Formula: see text], and [Formula: see text] (where [Formula: see text], [Formula: see text], [Formula: see text] being real constants and [Formula: see text] a positive integer) have been studied. The corresponding energy conditions are worked out and are analyzed graphically in the presence of the conformal motion with Lorentzian source. The presence of the exotic matter has been confirmed due to the violation of null energy conditions under some particular conditions, thereby proving the existence of the wormhole geometries in both of the models under investigation. Moreover, the stability of the wormhole geometries via the Tolman-Oppenheimer-Volkov equation has been discussed. It is concluded that these wormhole solutions supported by the non-exotic matter truly exist and are well stable under the extended teleparallel gravity.

Cosmological implications and thermodynamics of some reconstructed modified gravity models

Abstract In the context of extended teleparallel gravity theory with Gauss–Bonnet term, we reconstruct some gravitational Lagrangian functions f ( T , T G ) = T G g ( T ) and f ( T , T G ) = − T + T G g ( T ) , using some holographic dark energy models. These models include Tsallis, Renyi and Sharma–Mittal holographic dark energy models. We consider the flat FRW universe model with perfect fluid. We check the behavior of these reconstructed models through equation of state parameter for dark energy dominated era along with its plane of evolutionary parameter to check the thawing and freezing regions. In order to check the stability of the models, we explore the squared speed of sound for these models. Also, we discuss the thermodynamical analysis by checking the validity of generalized second law of thermodynamics of these reconstructed models.

Flat Connection for Rotating Vacuum Spacetimes in Extended Teleparallel Gravity Theories

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.

Noether symmetries and boundary terms in extended Teleparallel gravity cosmology

We discuss an extended Teleparallel gravity models comprising functions of scalar invariants constructed by torsion, torsion Gauss–Bonnet and boundary terms. We adopt the Noether symmetry approach to select the functional forms, the first integrals and, eventually, the exact solutions of the dynamics in the context of flat Friedman–Robertson–Walker cosmology. Standard perfect fluid matter, minimally coupled to geometry, is considered. Several physically consistent models are derived with related exact solutions.

Dynamics of evolving self-gravitating models in extended teleparallel gravity

The self-gravitating spherically symmetric fluid models are being studied taking power-law model in extended teleparallel (or [Formula: see text]) gravity. We form a set of governing equations which describes the dynamics of stellar evolution in the presence of torsion scalar (dark energy candidate) by incorporating power-law model in [Formula: see text] gravity along with dynamical terms like shear tensor, anisotropy, expansion scalar, dissipation, Weyl tensor and energy inhomogeneity. We explore some particular models of fluid according to various dynamical scenarios for particular values of model parameter [Formula: see text]. It is found that torsion terms associated with [Formula: see text], govern stellar evolution and provide deviation from theory of general relativity (GR). For the case, [Formula: see text], tetrad field is almost negligible and the evolving models are consistent with GR model having cosmological constant. We obtain practicable rate of change of expansion and deformation of fluid models at [Formula: see text].

Cosmological bouncing solutions in extended teleparallel gravity theories

In the context of extended Teleparallel gravity theories with a 3+1 dimensions Gauss-Bonnet analog term, we address the possibility of these theories reproducing several well-known cosmological bouncing scenarios in a four-dimensional Friedmann-Lema\^itre-Robertson-Walker geometry. We shall study which types of gravitational Lagrangians are capable of reconstructing bouncing solutions provided by analytical expressions for symmetric, oscillatory, superbounce, the matter bounce and singular bounce. Some of the Lagrangians discovered are both analytical at the origin having Minkowski and Schwarzschild as vacuum solutions. All these results open the possibility up for such theories to be competitive candidates of extended theories of gravity in cosmological scales.

Cosmological reconstructed solutions in extended teleparallel gravity theories with a teleparallel Gauss–Bonnet term

In the context of extended teleparallel gravity theories with a 3 + 1 dimensions Gauss–Bonnet analog term, we address the possibility of these theories reproducing several well-known cosmological solutions. In particular when applied to a Friedmann–Lemaître–Robertson–Walker geometry in four-dimensional spacetime with standard fluids exclusively. We study different types of gravitational Lagrangians and reconstruct solutions provided by analytical expressions for either the cosmological scale factor or the Hubble parameter. We also show that it is possible to find Lagrangians of this type without a cosmological constant such that the behaviour of the ΛCDM model is precisely mimicked. The new Lagrangians may also lead to other phenomenological consequences opening up the possibility for new theories to compete directly with other extensions of General Relativity.

Exponential and logarithmic f(T) wormhole solutions in Lorentzian noncommutative background

In this paper, we take noncommutative geometry under Lorentzian distribution and explore static spherically symmetric wormhole solutions in the extended teleparallel gravity by taking exponential and logarithmic f (T) models. For matter components, we use effective energy-momentum tensor for a nondiagonal tetrad and develop field equations. We work to explore solutions by considering various viable f(T) models and conclude that there exists a possibility of physically acceptable wormhole solutions under noncommutative background for these models. We observe that the effective energy-momentum tensor is responsible for the violation of the energy conditions. Also, we check the stability for these solutions by equilibrium condition. The equilibrium condition does not meet properly for any obtained solutions. Therefore solutions are in less equilibrium situation.