Traversable wormhole solutions in f(R,T) gravity with three novel shape functions

2021 ◽  
Author(s):  
Nisha Godani
Keyword(s):  
Shape Functions ◽  
Traversable Wormhole

Existence of dynamical wormholes in f(R) gravity

2020 ◽  
Vol 98 (5) ◽  
pp. 474-483
Author(s):  
Z. Yousaf ◽  
A. Ikram ◽  
M. Ilyas ◽  
M.Z. Bhatti
Keyword(s):  
Graphical Analysis ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Shape Functions ◽  
Field Equations ◽  
Ordinary Matter ◽  
Traversable Wormhole ◽  
Traversable Wormholes ◽  
Fluid Configuration

This paper explores spherically symmetrical dynamical traversable wormhole solutions for an anisotropic fluid configuration in the context of f(R) gravity. We construct the corresponding field equations and investigate the wormhole solutions by specifying the redshift and shape functions for three models of f(R) gravity. Graphical analysis shows that ordinary matter satisfies the null as well as weak energy conditions against the time and radial coordinates for each model. It is concluded that dynamical traversable wormholes are supported by this theory.

scholarly journals Traversable wormhole solutions in f(R) gravity via Karmarkar condition

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
M. Farasat Shamir ◽  
I. Fayyaz
Keyword(s):  
Gravity Model ◽  
Shape Function ◽  
Three Dimensional ◽  
Gravity Models ◽  
Dimensional Euclidean Space ◽  
Spherically Symmetric ◽  
Shape Functions ◽  
Traversable Wormhole ◽  
Asymptotically Flat ◽  
Free Parameters

AbstractMotivated by recent proposals of possible wormhole shape functions, we construct a wormhole shape function by employing the Karmarkar condition for static traversable wormhole geometry. The proposed shape function generates wormhole geometry that connects two asymptotically flat regions of spacetime and satisfies the required conditions. Further, we discuss the embedding diagram in three-dimensional Euclidean space to present the wormhole configurations. The main feature of current study is to consider three well-known f(R) gravity models, namely exponential gravity model, Starobinsky gravity Model and Tsujikawa f(R) gravity model. Moreover, we investigate that our proposed shape function provides the wormhole solutions with less (or may be negligible) amount of exotic matter corresponding to the appropriate choice of f(R) gravity models and suitable values of free parameters. Interestingly, the solutions obtained for this shape function generate stable static spherically symmetric wormhole structure in the context of non-existence theorem in f(R) gravity. This may lead to a better analytical representation of wormhole solutions in other modified gravities for the suggested shape function.

Traversable wormhole modelling with exponential and hyperbolic shape functions in F(R,T) framework

2020 ◽  
Vol 35 (25) ◽  
pp. 2050149
Author(s):  
Shweta ◽  
Ambuj Kumar Mishra ◽  
Umesh Kumar Sharma
Keyword(s):  
Shape Function ◽  
Energy Condition ◽  
Gravitational Theory ◽  
Null Energy Condition ◽  
Relativity Theory ◽  
Shape Functions ◽  
Traversable Wormhole ◽  
Hydrostatic Force ◽  
State Formula ◽  
The Stability

The concept of traversable wormhole, a hypothetical tunnel-like structure is initially proposed by Morris and Thorne (Am. J. Phys. 56, 395 (1988)) by using Einstein’s general relativity theory. Harko et al. (Phys. Rev. D 84, 024020 (2011)) defined [Formula: see text] gravity as an extended gravitational theory having terms [Formula: see text] and [Formula: see text] as Ricci scalar and trace of energy momentum respectively. In this article, we explore wormhole models for the framework of [Formula: see text] gravity by using two different shape functions. The first shape function is [Formula: see text], [Formula: see text] (proposed by Mishra and Sharma, arXiv:2003.00298v1 , 2020) and second is a hyperbolic shape function which is of the form [Formula: see text]. Geometrical behavior of wormholes are discussed in anisotropic scenario by using equation of state [Formula: see text]. The stability of models are analyzed by using equilibrium condition and determining gravitational force, anisotropic force, hydrostatic force and force due to modified gravity. For the validation of null energy condition and weak energy condition, significant role of shape function is illustrated for the presence of nonexotic matter.

scholarly journals Higher Order Multiscale Finite Element Method for Heat Transfer Modeling

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3827
Author(s):  
Marek Klimczak ◽  
Witold Cecot
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Higher Order ◽  
Shape Functions ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Steady State Heat ◽  
Steady State Heat Transfer

In this paper, we present a new approach to model the steady-state heat transfer in heterogeneous materials. The multiscale finite element method (MsFEM) is improved and used to solve this problem. MsFEM is a fast and flexible method for upscaling. Its numerical efficiency is based on the natural parallelization of the main computations and their further simplifications due to the numerical nature of the problem. The approach does not require the distinct separation of scales, which makes its applicability to the numerical modeling of the composites very broad. Our novelty relies on modifications to the standard higher-order shape functions, which are then applied to the steady-state heat transfer problem. To the best of our knowledge, MsFEM (based on the special shape function assessment) has not been previously used for an approximation order higher than p = 2, with the hierarchical shape functions applied and non-periodic domains, in this problem. Some numerical results are presented and compared with the standard direct finite-element solutions. The first test shows the performance of higher-order MsFEM for the asphalt concrete sample which is subject to heating. The second test is the challenging problem of metal foam analysis. The thermal conductivity of air and aluminum differ by several orders of magnitude, which is typically very difficult for the upscaling methods. A very good agreement between our upscaled and reference results was observed, together with a significant reduction in the number of degrees of freedom. The error analysis and the p-convergence of the method are also presented. The latter is studied in terms of both the number of degrees of freedom and the computational time.

scholarly journals Traversable wormhole in coupled Sachdev-Ye-Kitaev models with imbalanced interactions

2021 ◽  
Vol 104 (3) ◽  
Author(s):  
Rafael Haenel ◽  
Sharmistha Sahoo ◽  
Timothy H. Hsieh ◽  
Marcel Franz
Keyword(s):  
Traversable Wormhole

scholarly journals Traversable Wormhole Geometries in Gravity

2021 ◽  
pp. 2100023
Author(s):  
Zinnat Hassan ◽  
Sanjay Mandal ◽  
P.K. Sahoo
Keyword(s):  
Traversable Wormhole

MESHFREE CELL-BASED SMOOTHED POINT INTERPOLATION METHOD USING ISOPARAMETRIC PIM SHAPE FUNCTIONS AND CONDENSED RPIM SHAPE FUNCTIONS

2011 ◽  
Vol 08 (04) ◽  
pp. 705-730 ◽  
Author(s):  
G. Y. ZHANG ◽  
G. R. LIU
Keyword(s):  
Computational Efficiency ◽  
Interpolation Method ◽  
Shape Functions ◽  
Generalized Gradient ◽  
Singularity Problem ◽  
Numerical Examples ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
System Equations ◽  
Gradient Smoothing

This paper presents two novel and effective cell-based smoothed point interpolation methods (CS-PIM) using isoparametric PIM (PIM-Iso) shape functions and condensed radial PIM (RPIM-Cd) shape functions respectively. These two types of PIM shape functions can successfully overcome the singularity problem occurred in the process of creating PIM shape functions and make the constructed CS-PIM models work well with the three-node triangular meshes. Smoothed strains are obtained by performing the generalized gradient smoothing operation over each triangular background cells, because the nodal PIM shape functions can be discontinuous. The generalized smoothed Galerkin (GS-Galerkin) weakform is used to create the discretized system equations. Some numerical examples are studied to examine various properties of the present methods in terms of accuracy, convergence, and computational efficiency.

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