Traversable Wormholes and Energy Conditions with Two Different Shape Functions in $f(R)$ Gravity

Abstract

Traversable wormholes, tunnel like structures introduced by Morris \& Thorne \cite{morris1}, have a significant role in connection of two different space-times or two different parts of the same space-time. The characteristics of these wormholes depend upon the redshift and shape functions which are defined in terms of radial coordinate. In literature, several shape functions are defined and wormholes are studied in $f(R)$ gravity with respect to these shape functions \cite{lobo, saiedi, baha}. In this paper, two shape functions (i) $b(r)=\frac{r_0\log (r+1)}{\log (r_0+1)}$ and (ii) $b(r)=r_0(\frac{r}{r_0}{)}^{\gamma }$, $0<\gamma <1$ are considered. The first shape function is newly defined, however the second one is collected from the literature\cite{cataldo}. The wormholes are investigated for each type of shape function in $f(R)$ gravity with $f(R)=R+\alpha R^m-\beta R^{-n}$, where $m$, $n$, $\alpha$, and $\beta$ are real constants. Varying parameters $\alpha$ or $\beta$, $f(R)$ model is studied in five subcases for each type of shape function. In each case, the energy density, radial \& tangential pressures, energy conditions that include null energy condition, weak energy condition, strong energy condition \& dominated energy condition, and anisotropic parameter are computed. The energy density is found to be positive and all energy conditions are obtained to be violated which supports the existence of wormholes. Also, the equation of state parameter is obtained to possess values less than -1, that shows the presence of the phantom fluid and leads towards the expansion of the universe.

25 pages, 80 figures, Accepted in IJMPD

References in corpus (66)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• f(R) theories
• Introduction to Modified Gravity and Gravitational Alternative for Dark Energy
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Wormhole geometries in f(R) modified theories of gravity
• Morris-Thorne wormholes with a cosmological constant
• f(R) Gravity and scalar-tensor theory
• Einstein-Gauss-Bonnet traversable wormholes satisfying the weak energy condition
• Chaplygin traversable wormholes
• The role of energy conditions in $f(R)$ cosmology
• Analytical general solutions for static wormholes in $f(R,T)$ gravity
• The realistic models of relativistic stars in f(R) = R + alpha R^2 gravity
• Shadows of rotating wormholes
• Static wormhole solution for higher-dimensional gravity in vacuum
• Nearly Starobinsky inflation from modified gravity
• Inflationary universe from perfect fluid and $F(R)$ gravity and its comparison with observational data
• Self-consistent Wormhole Solutions of Semiclassical Gravity
• A polynomial f(R) inflation model
• Traversable wormholes satisfying the weak energy condition in third-order Lovelock gravity
• Palatini Formulation of Modified Gravity with $\ln R$ Terms
• Dynamical Systems Perspective of Cosmological Finite-time Singularities in $f(R)$ Gravity and Interacting Multifluid Cosmology
• Role of Tilted Congruence and $f(R)$ Gravity on Regular Compact Objects
• Wormhole throats in $R^m$ gravity
• $f(R)$ constant-roll inflation
• Unification of inflation and cosmic acceleration in the Palatini formalism
• Higher-dimensional evolving wormholes satisfying the null energy condition
• The Finslerian wormhole models
• Cosmological wormholes in $f(R)$ theories of gravity
• Complexity Factor For Static Anisotropic Self-Gravitating Source in $f(R)$ Gravity
• Deceleration versus Acceleration Universe in Different Frames of $F(R)$ Gravity
• N-dimensional static and evolving Lorentzian wormholes with cosmological constant
• Wormholes minimally violating the null energy condition
• Induced wormholes due to quantum effects of spherically reduced matter in large N approximation
• Wormholes supported by phantom-like modified Chaplygin gas
• Can primordial wormholes be induced by GUTs at the early Universe?
• Anisotropic cosmological solutions in $R+R^2$ gravity
• Time-Dependent Wormhole Solutions of $f(R)$ Theory of Gravity and Energy Conditions
• Can structure formation distinguish ΛCDM from non-minimal f(R) Gravity?
• Novel third-order Lovelock wormhole solutions
• Generic feature of future crossing of phantom divide in viable $f(R)$ gravity models
• Wormholes in f(R) gravity with a noncommutative-geometry background
• Wormhole geometries supported by three-form fields
• Wormhole Geometry and Noether Symmetry in f(R) Gravity
• Linear stability analysis of a rotating thin-shell wormhole
• Modified Chaplygin Traversable Wormholes
• Statefinder diagnostic and constraints on the Palatini f(R) gravity theories
• New inhomogeneous universes in scalar-tensor and f(R) gravity
• Higher Dimensional Inhomogeneous Perfect Fluid Collapse in \emph{f(R)} Gravity
• Domain wall solution in $F(R)$ gravity and variation of the fine structure constant
• Phantom crossing in viable $f(R)$ theories
• Palatini wormholes and energy conditions from the prism of General Relativity
• Action Growth in $f\left(R\right)$ Gravity
• Lemaitre-Tolman-Bondi dust solutions in f(R) gravity
• Reconstruction method of $f(R)$ gravity for isotropic and anisotropic spacetimes
• Exponential Inflation with $F(R)$ Gravity
• New integrable models and analytical solutions in $f(R)$~cosmology with an ideal gas
• Uniqueness of higher-dimensional phantom field wormholes
• Black Hole Topology in $f(R)$ Gravity
• Five dimensional cosmological traversable wormhole
• Weakly Charged Compact Stars in $f\left(R\right)$ gravity
• Stable Palatini $f(\mathcal{R})$ braneworld
• Characteristic Formulation for Metric $f(R)$ Gravity
• Viability of Arctan Model of f(R) Gravity for Late-time Cosmology

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• Strong gravitational lensing by wormholes
• Validation of Energy Conditions in Wormhole Geometry within Viable $f(R)$ Gravity
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• Traversable Wormhole Solutions in $f(R)$ Gravity Via Karmarkar Condition
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• Wormhole Modeling Supported by Non-Exotic Matter
• Investigation of Traversable Wormhole Solutions in Modified $f(R)$ Gravity with Scalar Potential
• Charged wormholes in f(R,T) extended theory of gravity
• Quasi-normal modes of bumblebee wormhole
• Stability analysis for cosmological models in $f(R)$ gravity using dynamical system analysis
• Existence of Wormhole Solutions in $f(Q,T)$ Gravity under Non-commutative Geometries
• Traversable Wormholes in $f(R,T)$ Gravity
• FRW Cosmology in $f(Q,T)$ Gravity
• Static Traversable Wormholes in $f(R,T)=R+2\alpha \ln T$ Gravity
• Morris-Thorne Wormholes in $f(R,T)$ modified theory of gravity
• Wormhole solutions with a polynomial equation-of-state and minimal violation of the null energy condition
• Traversable wormholes in $f(R)$-massive gravity
• Charged traversable wormholes supported by Casimir energy with and without GUP corrections
• Impact of dark matter galactic halo models on wormhole geometry within $f(Q,T)$ gravity
• Traversable wormholes in the traceless $f(R,T)$ gravity
• An exponential shape function for wormholes in modified gravity
• Traversable wormholes with logarithmic shape function in f(R, T) gravity
• Physical Parameters for Stable $f(R)$ Models
• Wormhole solution in modified teleparallel-Rastall gravity and energy conditions
• Estimation of Cosmological Parameters, Stability Analysis and Energy Conditions in Viable Modified Gravity
• A new shape function for wormholes in $f(R)$ gravity and General Relativity
• Non-commutative Wormholes in $f(R)$ Gravity satisfying the Energy Conditions
• Traversable wormhole in logarithmic $f(R)$ gravity by various shape and redshift functions
• Generalised Ellis-Bronnikov wormholes embedded in warped braneworld background and energy conditions
• Morris-Thorne-type wormhole with global monopole charge and the energy conditions
• Wormhole solutions in $f(R)$ gravity theory for Chaplygin gas scenario
• Phantom energy supported wormhole model in $f(R,T)$ gravity assuming conformal motion
• Wormhole modeling in $R^2$ gravity with linear trace term
• Validity of energy conditions of matter in traversable wormholes under the $f(Q)$ modified gravity theory
• Cosmological dynamics of f(R) models in dynamical system analysis
• New Wormhole Solutions in a Viable $f(R)$ Gravity Model
• Non-exotic wormholes in 4-D Einstein-Gauss-Bonnet gravity
• Viable Wormhole Structures and Energy Conditions in f(Q,T) Theory
• Evolving Wormholes in a Cosmological Background
• Dynamical Formation of Charged Wormholes
• Traversable wormholes in $f(R)$ gravity sourced by a cloud of strings
• Traversable Wormholes induced by polytropic $n=1$ energy density
• Charged galactic wormholes: shadow imaging, accretion disks, and charged-particle deflection
• Energy Conditions and Stability of Charged Wormholes in $f(R,{\mathcal{L}}_m)$ Gravity: A Comparative Analysis with Compact Objects