General Teleparallel Gravity Research Articles

Gauge-invariant cosmological perturbations in general teleparallel gravity

We study linear cosmological perturbations in the most general teleparallel gravity setting, where gravity is mediated by the torsion and nonmetricity of a flat connection alongside the metric. For a general linear perturbation of this geometry around a homogeneous and isotropic background geometry, we derive the irreducible decomposition of the perturbation variables, as well as their behavior under gauge transformations, i.e., infinitesimal diffeomorphisms generated by a vector field. In addition, we also study these properties for the most general set of matter variables and gravitational field equations. We then make use of these result to construct gauge-invariant perturbation variables, using a general approach based on gauge conditions. We further calculate these quantities also in the metric and symmetric teleparallel geometries, where nonmetricity or torsion is imposed to vanish. To illustrate our results, we derive the energy-momentum–hypermomentum conservation equations for both the cosmological background and the linear perturbations. As another example, we study the propagation of tensor perturbations in the f(G), f(T) and f(Q) class of theories.

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.

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.

Kalb-Ramond field-induced cosmological bounce in generalized teleparallel gravity

One of the important open questions in high-energy physics is to understand the lack of evidence of the Kalb-Ramond (KR) field, in particular in present day cosmology. In this paper we aim to address this issue by showing that a bounce scenario in the evolution of the Universe strongly advocates their elusiveness, even if their energy density was very large to start with. We consider the Kalb-Ramond field and its effects in the context of generalized teleparallel gravity in ($3+1$) dimensions. Teleparallel gravity is a description of gravitation in which the tetrads are the dynamical degrees of freedom, and the torsion arising from fields with spin are accommodated naturally as field strength tensors. In order to describe the coupling prescription, we address the correct generalization of the Fock-Ivanenko derivative operator for an $n$-form tensor field. By varying with respect to the tetrads, this rank-2 field is shown to source the teleparallel equivalent of Einstein's equations. We study the possibility of reproducing two well-known cosmological bounce scenarios; namely, symmetric bounce and matter bounce in four-dimensional spacetime with the Friedmann-Lema\^{\i}tre-Robertson-Walker metric, and observe that the solution requires the KR field energy density to be localized near the bounce. The crucial result in our work is that this feature also naturally explains the lack of cosmological evidence of the rank-2 field in the present day Universe for the matter-bounce scenario. Thus, among the bouncing cosmologies, the latter is favored over the former.

Energy contents of stringy charged black hole in general relativity and teleparallel gravity

In the framework of general relativity (GR) and teleparallel equivalent to GR (TEGR), we investigate the energy–momentum localization of a stringy charged black hole by using Bergman–Thompson’s prescription and the Papapetrou’s prescription. Moreover, we investigate the gravitational energy–momentum (GEM) in TEGR. Our results are consistent with the results of previous studies. Finally, we calculate the GEM flux and gravitational center of mass in TEGR.

Gravitational waves in higher order teleparallel gravity

The teleparallel equivalent of higher order Lagrangians like L □R = −R + a 0 R 2 + a 1 R□R can be obtained by means of the boundary term B = 2∇ μ T μ . In this perspective, we derive the field equations in presence of matter for higher-order teleparallel gravity considering, in particular, sixth-order theories where the □ operator is linearly included. In the weak field approximation, gravitational wave solutions for these theories are derived. Three states of polarization are found: the two standard + and × polarizations, namely 2-helicity massless transverse tensor polarizations, and a 0-helicity massive, with partly transverse and partly longitudinal scalar polarization. Moreover, these gravitational waves (GWs) exhibit four oscillation modes related to four degrees of freedom: the two classical + and × tensor modes of frequency ω 1, related to the standard Einstein waves with ; two mixed longitudinal-transverse scalar modes for each frequencies ω 2 and ω 3, related to two different 4-wave vectors, and . The four degrees of freedom are the amplitudes of each individual mode, i.e. , , , and . To describe a general teleparallel gravity model of order (2p + 2), we used the teleparallel Lagrangian which demonstrates to be not equivalent to . By varying its action, the related field equations in the presence of matter are derived. Hence we obtain the GWs for these teleparallel gravity models, i.e. , that are exactly the Einstein GWs as in f(T) teleparallel gravity. In conclusion, the boundary term B generates extra polarizations and additional modes beyond the standard ones. In particular B 2 and B□B terms generate both the additional scalar polarization and the extra scalar modes.

Propagation of gravitational waves in teleparallel gravity theories

We investigate propagation of gravitational waves in the most general teleparallel gravity model with second order field equations around the Minkowski background. We argue that in this case the most general Lagrangian at the first order of perturbations is given by the linear combination of quadratic invariants and hence coincides with the well-known new general relativity model. We derive the linearized field equations and analyze them using the principal polynomial and the Newman-Penrose formalism. We demonstrate that all gravitational wave modes propagate at the speed of light and there are up to six possible polarizations. We show that two tensorial modes of general relativity are always present and the number of extra polarizations depends on the free parameters of the new general relativity model.

F(T) Corrected Instability of Cylindrical Collapsing Object with Harrison-Wheeler Equation of State

We study the dynamical instability of a collapsing object in the framework of generalized teleparallel gravity. We assume a cylindrical object with a specific matter distribution. This distribution contains energy density and isotropic pressure component with heat conduction. We take oscillating states scheme up to first order to check the instable behavior of the object. We construct a general collapse equation for underlying case with nondiagonal tetrad depending on the matter, metric functions, heat conducting term, and torsional terms. The Harrison-Wheeler equation of state which contains adiabatic index is used to explore the dynamical instability ranges for Newtonian and post-Newtonian constraints. These ranges depend on perturbed part of metric coefficients, matter parts, and torsion.

Generic phase portrait analysis of finite-time singularities and generalized Teleparallel gravity**Supported by the Egyptian Ministry of Scientific Research (24-2-12)

We analyze the four common types of finite-time singularity using a generic framework of the phase portrait geometric approach. This technique requires the Friedmann system to be written as a one-dimensional autonomous system. We employ a scale factor that has been used widely in the literature to realize the four finite-time singularity types, then we give a detailed discussion for each case showing possible novel models. Moreover, we show how different singularity types can play essential roles in different cosmological scenarios. Among several modified gravity theories, we show that the f(T) cosmology is compatible with the phase portrait analysis, since the field equations include Hubble derivatives only up to first order. Therefore, we reconstruct the f(T) theory which generates these phase portraits. We also perform a complementary analysis using the effective equation of state. Furthermore, we investigate the role of the torsion fluid in realizing the cosmic singularities.

Gravitational collapse in generalized teleparallel gravity

The idea of this work is to exhibit the unstable regions of a self-gravitating celestial object which collapses adiabatically with a non-vanishing expansion scalar. We adopted the generalized teleparallel gravity for a plane-symmetric self-gravitating object and matter distribution as dissipative and anisotropic. We analyzed the instability regions of the stellar model by considering a particular model, i.e., $\beta T + \gamma T^{n}$ . We established the basic dynamical equations together with junction conditions and equation of state proposed by Harrison et al. The linear perturbation strategy is applied to the metric, matter and f (T) function up to first order. The equations of motion are developed under this perturbative framework to construct collapse equation. We demonstrate the unstable phases at weak field limit and post-Newtonian epochs and deduce a vital role of adiabatic index to explain the stability/instability issues for planar model in f (T) gravity.

Generalized teleparallel cosmology and initial singularity crossing

We present a class of cosmological solutions for a generalized teleparallel gravity with f(T)=T+α̃ (−T)n, where α̃ is some parameter and n is an integer or half-integer. Choosing α̃ ∼ Gn−1, where G is the gravitational constant, and working with an equation of state p=w ρ, one obtains a cosmological solution with multiple branches. The dynamics of the solution describes standard cosmology at late times, but the higher-torsion correction changes the nature of the initial singularity from big bang to a sudden singularity. The milder behavior of the sudden singularity enables us to extend timelike or lightlike curves, through joining two disconnected branches of solution at the singularity, leaving the singularity traversable. We show that this extension is consistent with the field equations through checking the known junction conditions for generalized teleparallel gravity. This suggests that these solutions describe a contracting phase a prior to the expanding phase of the universe.

Inflation with teleparallelism: Can torsion generate primordial fluctuations without local Lorentz symmetry?

Arbitrary generalization to the teleparallel equivalent of general relativity loses local Lorentz invariance to reparametrize the orthonormal coordinate system and gives rise to asymmetry field equations. We investigate consequences of local Lorentz violation to primordial fluctuations in extended single field inflationary models based on the scalar-tensor formulation of the torsion scalar $T$ that effectively includes $f(T)$ gravity as a special case. We show that despite some asymmetry part of the field equations are removed in a spatially homogeneous and isotropic cosmic background, no subhorizon scalar-perturbation mode can survive by the time of horizon crossing. As a result, any scalar field mediated in torsion cannot generate enough primordial density inhomogeneity alone, even if it brings some de Sitter background solutions in generalized teleparallel gravity.

Dynamical instability of cylindrical symmetric collapsing star in generalized teleparallel gravity

This paper is devoted to analyze the dynamical instability of a self-gravitating object undergoes to collapse process. We take the framework of generalized teleparallel gravity with cylindrically symmetric gravitating object. The matter distribution is represented by locally anisotropic energy-momentum tensor. We develop basic equations such as dynamical equations along with matching conditions and Harrison-Wheeler equation of state. By applying linear perturbation strategy, we construct collapse equation which is used to accomplish the instability ranges in Newtonian and post-Newtonian regimes. We find these ranges for isotropic pressure as well as reduce the results in general relativity. The unstable behavior depends on matter, metric, mass and torsion based terms.

Cosmological evolution of generalized ghost pilgrim dark energy in f ( T ) $f(T)$ gravity

We explore the phenomenon that phantom-like dark energy prevents the formation of black holes by assuming the generalized ghost version of pilgrim dark energy in the background of generalized teleparallel gravity. In this scenario, we construct \(f(T)\) model for explaining the evolutionary behavior of equation of state parameter, \(\omega_{\varLambda}-\omega'_{\varLambda}\) and \(r-s\) planes. We discuss these cosmological parameters graphically by taking different values of redshift parameter and pilgrim dark energy parameter. It is found that the equation of state parameter shows phantom like behavior while \(\omega_{\varLambda}-\omega'_{\varLambda}\) plane possesses thawing region for some particular values of pilgrim dark energy parameter. The statefinder parameters in \(r-s\) plane indicate the behavior of quintessence and phantom models. Finally, we discuss the first and second laws of thermodynamics and investigate the behavior of entropy production term.

Trace-anomaly driven inflation in f(T) gravity with a cosmological constant

In this paper, we have investigated trace-anomaly (TA) driven inflation in Generalized Teleparallel gravity (namely f(T)). A quasi de Sitter (dS) scenario for inflation is proposed like in the case of R 2 gravity. It has been found that in f(T) gravity, the dS solution for inflation is unstable due to the conformal anomaly (CA). As an illustrative example, we have analyzed trace anomaly driven inflation in a T 2+f(T)-model. Furthermore, a model with a non zero cosmological constant is studied. We have shown that dS solution always remains unstable also in the presence of cosmological constant, but for Anti dS (AdS) case the situation dramatically changes.

Evaporation phenomena in f(T) gravity

We formulate evaporation phenomena in a generic model of generalized teleparallel gravity in Weitzenbock space–time with a diagonal and nondiagonal tetrad basis. We also perform perturbation analysis around the constant torsion scalar solution called the Nariai space–time, which is an exact solution of the field equations as the limiting case of the Schwarzschild – de Sitter space–time and in the limit where two black holes and their cosmological horizons coincide. By a carefully analysis of the horizon perturbation equation, we show that (anti)evaporation cannot happen if we use a diagonal tetrad basis. This result implies that a typical black hole in any generic form of generalized teleparallel gravity is frozen in its initial state if we use diagonal tetrads, but in the case of nondiagonal tetrads the analysis is completely different. With a suitable nontrivial nondiagonal tetrad basis we investigate the linear stability of the model under simultaneous perturbations of the metric and torsion. We observe that in spite of the diagonal case, both evaporation and antievaporation can happen. These phenomena depend on the initial phase of the horizon perturbation. In the first mode, when we restrict ourselves to the first lower modes (anti)evaporation takes place. So, in the nondiagonal case, the physical phenomena are reasonable. This is an important advantage of using nondiagonal tetrads instead of diagonal ones. We also see that this is a universal feature, completely independent from the form of the model.

First-order formalism for thick branes in modified teleparallel gravity

This work deals with braneworld scenarios with generalized teleparallel gravity. We extend a recent investigation, where the model studied was described by $F(T)=T+k{T}^{n}$. In the current study, we introduce the first-order formalism to find analytical solutions for models that include a scalar field with standard and generalized dynamics. In particular, we describe the interesting case in which the brane splits, due to the parameters that control deviation from the standard model.

Acausality and nonunique evolution in generalized teleparallel gravity

We show the existence of physical superluminal modes and acausality in the Brans-Dicke type of extension of teleparallel gravity that includes F(T) gravity and teleparallel dark energy as special cases. We derive the characteristic hypersurface for the extra degrees of freedom in the theory, thereby showing that the time evolution is not unique and closed causal curves can appear. Furthermore, we present a concrete disastrous solution in Bianchi type I spacetime, in which the anisotropy in expansion can be any function of time, and thus anisotropy can emerge suddenly, a simple demonstration that the theory is physically problematic.

Galactic Halo Wormhole Solutions inf(T)Gravity

The proposal of galactic halo region is based on the idea that dark halos contain some characteristics needed to support traversable wormhole solutions. We explore wormhole solutions in this region in the framework of generalized teleparallel gravity. We consider static spherically symmetric wormhole spacetime with flat galactic rotational curves and obtain expressions of matter components for nondiagonal tetrad. The effective energy-momentum tensor leads to the violation of energy conditions which may impose condition on the normal matter to satisfy these conditions. We take two well-knownf(T)models in exponential and logarithmic forms to discuss wormhole solutions as well as the equilibrium condition. It is concluded that wormhole solutions violating weak energy condition are obtained for both models with stable configuration.

Charged black holes in generalized teleparallel gravity

In this paper we investigate charged static black holes in 4D for generalized teleparallel models of gravity, based on torsion as the geometric object for describing gravity according to the equivalence principle. As a motivated idea, we introduce a set of non-diagonal tetrads and derive the full system of non linear differential equations. We prove that the common Schwarzschild gauge is applicable only when we study linear f(T) case. We reobtain the Reissner-Nordstrom-de Sitter (or RN-AdS) solution for the linear case of f(T) and perform a parametric cosmological reconstruction for two nonlinear models. We also study in detail a type of the no-go theorem in the framework of this modified teleparallel gravity.