Teleparallel Gravity Research Articles

Influence of GUP corrected Casimir energy on zero tidal force wormholes in modified teleparallel gravity with matter coupling

In recent times, the study of the Casimir effect in quantum field theory has garnered increasing attention because of its potential to be an ideal source of exotic matter needed for stabilizing traversable wormholes. It has been confirmed through experimental evidence that this phenomenon involves fluctuations in the vacuum field, leading to a negative energy density. Motivated by the above, we have investigated Casimir wormholes with corrections from the Generalized Uncertainty Principle (GUP) within the framework of matter-coupled teleparallel gravity. Our analysis includes three well-known GUP models: the Kempf, Mangano, and Mann (KMM) model, the Detournay, Gabriel, and Spindel (DGS) model, and a third model called Model II. For a broader analysis, we have considered two well-known model functions for the teleparallel theory: a linear f(T,T)=αT+βT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T,\\mathcal {T})=\\alpha T+\\beta \\mathcal {T}$$\\end{document} and a quadratic model f(T,T)=ηT2+χT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T,\\mathcal {T})=\\eta T^2+\\chi \\mathcal {T}$$\\end{document}. The shape function solutions corresponding to both models are examined in the absence of tidal forces in spacetime. We also demonstrate the crucial role played by the parameters of the f(T,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T,\\mathcal {T})$$\\end{document} models in the violation of the energy conditions. With the increasing interest in detecting gravitational waves from astrophysical objects, we have thoroughly discussed the perturbation of the wormhole solutions in the scalar, electromagnetic, axial gravitational, and Dirac field backgrounds. We employ the 3rd order WKB expansion to find the complex frequencies associated with the quasinormal modes of energy dissipation. Additionally, we also calculate the active mass and total gravitational energy for the wormhole geometry. The amount of exotic matter involved in sustaining these wormholes is also found in this paper. Furthermore, the physical stability of such Casimir wormholes is examined using the Tolman–Oppenheimer–Volkoff equation.

Dynamical system analysis for scalar field potential in teleparallel gravity

AbstractIn this paper, we have presented a power law cosmological model and its dynamical system analysis in $$f(T,\phi )$$ f ( T , ϕ ) gravity, where T is the torsion scalar and $$\phi $$ ϕ is the canonical scalar field. The two well-motivated forms of the non-minimal coupling function $$F(\phi )$$ F ( ϕ ) , the exponential form and the power law form, with exponential scalar field potential, are investigated. The dynamical system analysis is performed by establishing the dimensionless dynamical variables, and the critical points were obtained. The evolution of standard density parameters is analysed for each case. The behaviour of the equation of state (EoS) and deceleration parameter agree with the result of recent cosmological observations. The model parameters are constrained using the existence and the stability conditions of the critical points describing different epochs of the evolution of the Universe.

Deflection of light by wormholes and its shadow due to dark matter within modified symmetric teleparallel gravity formalism

Abstract We explore the possibility of traversable wormhole formation in the dark matter halos in the context of $f(Q)$ gravity. We obtain the exact wormhole solutions with anisotropic matter source based on the Bose-Einstein condensate, Navarro-Frenk-White, and pseudo-isothermal matter density profiles. Notably, we present a novel wormhole solution supported by these dark matters using the expressions for the density profile and rotational velocity along with the modified field equations to calculate the redshift and shape functions of the wormholes. With a particular set of parameters, we demonstrate that our proposed wormhole solutions fulfill the flare-out condition against an asymptotic background. Additionally, we examine the energy conditions, focusing on the null energy conditions at the wormhole's throat, providing a graphical representation of the feasible and negative regions. Our study also examines the wormhole's shadow in the presence of various dark matter models, revealing that higher central densities result in a shadow closer to the throat, whereas lower values have the opposite effect. Moreover, we explore the deflection of light when it encounters these wormholes, particularly noting that light deflection approaches infinity at the throat, where the gravitational field is extremely strong.

Cosmology in energy-momentum squared symmetric teleparallel gravity

In this letter, we explore the f(Q,TμνTμν) gravity theory, building upon the foundations laid by the f(Q) and f(Q,T) gravity theories. Here, Q represents non-metricity and Tμν stands for the energy-momentum tensor. The proposed action encompasses an arbitrary function of both non-metricity Q and the square of the energy-momentum tensor, specifically T2=TμνTμν. We find the analytical solution for the barotropic fluid case p=ωρ for the model f(Q,TμνTμν)=Q+η(TμνTμν). We constrain parameters of the solution H(z) utilizing CC, BAO, and latest Pantheon+SH0ES samples with the help of Monte Carlo Markov Chain sampling technique along with Bayesian statistical analysis. Further, from the Om diagnostic test, we find that the assumed cosmological model favors the quintessence regime.

Anisotropic Spheres with Tolman–Kuchowicz Spacetime in the Context of f(Q,T)$f(Q,T)$ Gravity

AbstractThis study primarily focuses on exploring the nature of anisotropic spheres within the framework of extended symmetric teleparallel gravity. To accomplish this, an anisotropic matter distribution for gravity model with Tolman–Kuchowicz spacetime is considered. Through this analysis, the necessary conditions for matching the interior and exterior geometries of the spheres are discussed and calculated the values of the unknown parameters involved. Furthermore, the physical properties of these spheres are analyzed using observational data from compact objects. The results demonstrate that the interior solutions obtained for anisotropic spheres fulfill all requisite physical criteria, thereby ensuring the stability of our model.

On the Equivalence of Gravitational Waves Formulations in Teleparallel Gravity and General Relativity

Abstract Gravitational waves have become a vital way to test our current understanding of gravity. In this work, we explore the formulations of gravitational waves in two distinct theories of gravity: the Teleparallel Equivalent of General Relativity (TEGR), a subclass of Teleparallel Gravity (TG), and General Relativity (GR). By linearizing the gravitational field equations in each theory, we demonstrate that the formulations of gravitational waves in TEGR and GR are equivalent. This equivalence suggests that the teleparallel formalism can effectively describe gravitational waves, providing a novel perspective on the topic and potentially broadening the scope of gravitational wave research.

Impact of charge on the stability of pulsar SAX J1748.9-2021 in modified symmetric teleparallel gravity

In this paper, we explore the effect of charge on the stability of pulsar star SAX J1748.9-2021 in f(Q) gravity, where Q represents non-metricity. For this purpose, we apply the Krori-Barua metric ansatz with anisotropic fluid and use a linear f(Q) model f(Q)=ζQ, where ζ is a non-zero constant. We derive exact relativistic solutions of the corresponding field equations. Furthermore, we study its geometric and physical properties through astrophysical observations from the pulsar SAX J1748.9-2021, which is found in X-ray binary systems within globular clusters. We examine features like anisotropic pressure, the mass–radius relationship, redshift, the Zeldovich condition, energy and causality conditions, the adiabatic index, the Tolman–Oppenheimer–Volkoff equation, the equation of state parameter and compactness. Our findings align with the observational data which indicate that the pulsar SAX J1748.9-2021 is viable and stable under this modified theory of gravity.

Is spacetime curved? Assessing the underdetermination of general relativity and teleparallel gravity

Realism about general relativity (GR) seems to imply realism about spacetime curvature. The existence of the teleparallel equivalent of general relativity (TEGR) calls this into question, for (a) TEGR is set in a torsionful but flat spacetime, and (b) TEGR is empirically equivalent to GR. Knox (Stud Hist Philos Sci Part B Stud Hist Philos Mod Phys 42(4):264–275, 2011) claims that there is no genuine underdetermination between GR and TEGR; we call this verdict into question by isolating and addressing her individual arguments. In addition, we anticipate and evaluate two further worries for realism about the torsionful spacetimes of TEGR, which we call the ‘problem of operationalisability’ and the ‘problem of visualisability’.

Exploring cosmological evolution and constraints in [formula omitted] teleparallel gravity

This study explores the extension of teleparallel gravity within the framework of general relativity, introducing an algebraic function f(T) dependent on the torsion scalar T. Motivated by the teleparallel formulation, we investigate cosmological implications, employing the simplest parametrization of the dark energy equation of state. Our chosen f(T) function, f(T)=α(−T)n, undergoes stringent constraints using recent observational data (H(z), SNeIa, BAO, and CMB). The model aligns well with cosmic dynamics, exhibiting quintessence behavior. The evolution of the deceleration parameter, the behavior of dark energy components, and the Om(z) diagnostic further reveal intriguing cosmological phenomena, emphasizing the model’s compatibility with quintessence scenarios.

Static, cylindrically symmetric spacetime in the coincident f(Q) gravity

In this paper we consider a static, cylindrically symmetric spacetime with coincident f(Q) gravity. Since the field equation of this spacetime in symmetric teleparallel gravity is suitable for choosing the function of f(Q) in the form of power series and exponential forms which are in coherent with cosmological observations, anisotropic perfect fluid solutions of these forms are discussed for this spacetime. Energy densities, directional pressures and energy conditions are plotted and analysed for a few different metric potentials. Although corresponding cosmic strings violate all energy conditions in both f(Q) functions, the corresponding Levi-Civita solution violates all energy conditions in the power law function of f(Q), but for exponential f(Q) gravity they are satisfied in small regions.

Greybody factor of uncharged black hole in symmetric teleparallel gravity

In this study, we investigate the greybody factor of a (3+1)-dimensional black hole solution in the context of alternative f(Q) gravity with minimum scalar field coupling. We obtain the radial equation by applying the Klein–Gordon equation and transforming it into a Schrodinger wave equation using the tortoise coordinate. This transformation enables us to determine the effective potential and its graphical behavior for different values of the coupling constant and relevant physical parameters. We obtain two solutions for the radial equation corresponding to the event and cosmological horizons. To determine the greybody factor and its behavior, we combine these two solutions in the intermediate regime. The greybody factor increases with an increase in radius and coupling constant. This indicates that in alternative gravity, the larger black hole will die sooner as compared to cosmic gravity.

Stability and viability of charged anisotropic pulsar SAX J1748.9-2021 in extended symmetric teleparallel gravity

This manuscript aims to study the viability and stability of a pulsar SAX J1748.9-2021, containing a charged anisotropic matter configuration within the framework of f(Q,T) theory (Q and T are the non-metricity scalar and energy–momentum tensor, respectively). We employ a non-singular solution and a specific model of this gravitational theory and use junction conditions to determine the unknown constants in the metric coefficients. We explore different geometric and physical properties using astrophysical observations from the pulsar SAX J1748.9-2021, which is found in X-ray binary systems within globular clusters. This framework establishes relationships between various physical quantities, including fluid parameters, anisotropy, mass–radius relation, redshift, the Zeldovich condition, energy conditions, causality conditions, adiabatic index, Tolman–Oppenheimer–Volkoff equation, equation of state parameter and compactness. Our findings affirm the feasibility and stability of the proposed charged pulsar within this theoretical framework.

Teleparallel gravity and quintessence: The role of nonminimal boundary couplings

In this paper, we have outlined the development of an autonomous dynamical system within a general scalar-tensor gravity framework. This framework encompasses the overall structure of the non-minimally coupled scalar field functions for both the torsion scalar (T) and the boundary term (B). We have examined three well-motivated forms of potential functions and constrained the model parameters through dynamical system analysis. This analysis has played a crucial role in identifying cosmologically viable models. We have analysed the behaviour of dynamical parameters such as equation-of-state parameters, as well all the standard density parameters for radiation, matter, and dark energy to assess their compatibility with current observational data. The phase space diagrams are presented to support the stability conditions of the corresponding critical points. The Universe is apparent in its late-time cosmic acceleration phase via the dark energy-dominated critical points. Additionally, we compare our findings with the most prevailing ΛCDM model. The outcomes are further inspected using the cosmological data sets of Supernovae Ia and the Hubble rate H(z).

Scalar field induced dynamical evolution in teleparallel gravity

In this paper, we investigate the role of scalar field potentials in the dynamical evolution of the Universe. A gravity theory with a non-minimally coupled scalar field with torsion in the geometrical action simulating effective dark energy is considered to study an extended matter bounce scenario. The dynamical behaviour of the equation of state parameter has been studied near the bouncing epoch. Keeping in mind the inflationary behaviour near the bounce, five different scalar field potential functions are explored, and their effect on the equation of state parameter is investigated.

Stability analysis of static spherical spacetime in extended symmetric teleparallel gravity

Our manuscript aims to analyze the viability and stability of anisotropic stellar objects in the modified symmetric teleparallel gravity. A particular model of this extended theory is considered to formulate explicit field equations that govern the interaction between matter and geometry. The configuration of static spherical symmetric structures is examined through the Finch-Skea solution. However, the values of unknown constants in the metric potentials are evaluated by the Darmois junction conditions. For the viability of the proposed stellar objects, physical parameters including density, pressure, anisotropy, mass, energy constraints, compactness function, and redshift are analyzed. Furthermore, the stability of the proposed stellar objects is investigated by the causality condition, Herrera cracking approach, and adiabatic index. Our findings indicate that the proposed stellar objects are viable as well as stable in the presence of correction terms.

Degrees of Freedom in Modified Teleparallel Gravity

I discuss the issue of degrees of freedom in modified teleparallel gravity. These theories do have an extra structure on top of the usual (pseudo)Riemannian manifold, that of a flat parallel transport. This structure is absolutely abstract and unpredictable (pure gauge) in GRequivalent models, however, it becomes physical upon modifications. The problem is that, in the most popular models, this local symmetry is broken but not stably So, hence the infamous strong coupling issues. The Hamiltonian analyses become complicated and with contradictory results. A funny point is that what we see in available linear perturbation treatments of f (T) gravity is much closer to the analysis with less dynamical degrees of freedom which has got a well-known mistake in it, while the more accurate work predicts much more of dynamics than what has ever been seen till now. I discuss possible reasons behind this puzzle, and also argue in favor of studying the most general New GR models which are commonly ignored due to suspicion of ghosts.

Generalized ghost dark energy model in extended modified theory of symmetric teleparallel gravity

Generalized ghost dark energy model in extended modified theory of symmetric teleparallel gravity

Cosmological constraints on a dynamical dark energy model in F(Q) gravity

Extended teleparallel gravity, characterized by function F(Q), where Q is the non-metricity scalar, is one of the most promising approaches to general relativity. In this paper, we reexamine a specific dynamical dark energy model, which is indistinguishable from the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model at the present time and exhibits a special event in the future, within F(Q) gravity. To constrain the free parameters of the model, we perform Markov chain Monte Carlo (MCMC) analysis, using the last data from Pantheon+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Pantheon}^{+}$$\\end{document} and the latest measurements of the H(z) parameter, combined. On the basis of this analysis, we find that our dynamical dark energy model, in the context of F(Q) gravity, lies in the quintessence regime rather than in the phantom regime, as in the case of general relativity. Furthermore, this behavior affects the future expansion of the Universe, as it becomes decelerating at a 1σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\sigma $$\\end{document} confidence level for z<-0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z<-0.5$$\\end{document}, showing a bounce at zB≈-0.835\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z_{\ ext {B}}\\approx -0.835$$\\end{document}. We support our conclusion with a cosmographic analysis.

Rastall teleparallel gravity: gravitational decoupling with MGD approach

Rastall teleparallel gravity: gravitational decoupling with MGD approach

Modelling the accelerating universe with f(Q) gravity: observational consistency

In this paper, we present a cosmological model within the framework of symmetric teleparallel gravity, focusing on f(Q) gravity, where Q represents the non-metricity scalar. Utilizing cosmological datasets, we derive an accelerating cosmological model by constraining its free parameters. To achieve this, we determine the parametric form of the Hubble parameter using a well-motivated f(Q) function. Remarkably, all obtained values fall within the range suggested by cosmological observations. By employing the best-fit parameters, we calculate the present geometrical parameters and demonstrate the accelerating behaviour of the Universe. Furthermore, we thoroughly examine the evolutionary behaviours of the Universe, noting that our model converges to the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM model at late times. Finally, we investigate the energy conditions and find a violation of the strong energy condition, which could provide a valuable understanding of the nature of dark energy.