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

Department of Mathematics, Institute of Applied Sciences and Humanities, GLA University, Mathura-281 406, Uttar Pradesh, India

E-mail Address: shwetaibs84@gmail.com

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Ambuj Kumar Mishra

http://orcid.org/0000-0001-9059-6108

Department of Mathematics, Institute of Applied Sciences and Humanities, GLA University, Mathura-281 406, Uttar Pradesh, India

E-mail Address: ambuj_math@rediffmail.com

Corresponding author.

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, and

Umesh Kumar Sharma

Department of Mathematics, Institute of Applied Sciences and Humanities, GLA University, Mathura-281 406, Uttar Pradesh, India

E-mail Address: sharma.umesh@gla.ac.in

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https://doi.org/10.1142/S0217751X20501493Cited by:25 (Source: Crossref)

Abstract

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. D84, 024020 (2011)) defined $F (R, T)$ $F (R, T)$ gravity as an extended gravitational theory having terms $R$ $R$ and $T$ $T$ as Ricci scalar and trace of energy momentum respectively. In this article, we explore wormhole models for the framework of $F (R, T)$ $F (R, T)$ gravity by using two different shape functions. The first shape function is $b (r) = \frac{r_{0} a^{r}}{a^{r_{0}}}$ $b (r) = \frac{r_{0} a^{r}}{a^{r_{0}}}$ , $a \in (0, 1)$ $a \in (0, 1)$ (proposed by Mishra and Sharma, arXiv:2003.00298v1, 2020) and second is a hyperbolic shape function which is of the form $b (r) = \frac{r_{0} cosh (r_{0})}{cosh (r)}$ $b (r) = \frac{r_{0} cosh (r_{0})}{cosh (r)}$ . Geometrical behavior of wormholes are discussed in anisotropic scenario by using equation of state $ω = \frac{p_{r}}{ρ}$ $ω = \frac{p_{r}}{ρ}$ . 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.

Keywords:

PACS: 04.50.kd

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Vol. 35, No. 25

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Received 16 June 2020

Revised 10 August 2020

Accepted 11 August 2020

Published: 10 September 2020

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

Abstract

References

Traversable wormholes with exponential shape function in modified gravity and general relativity: A comparative study

Traversable wormhole models in modified theories of gravity

Yukawa–Casimir wormhole model in $F (R, T)$ framework

Energy conditions of traversable wormhole in the deformed $f (R)$ gravitational model

Traversable wormholes in Einsteinian-cubic-gravity with hybrid shape functions

Traversable wormhole solutions in $f (R, T)$ gravity with noncommutative geometry

Traversable wormhole solutions with non-exotic fluid in framework of $f (Q)$ gravity

Two different shape functions for wormholes in $f (R)$ theory with non-commutative geometry and Lorentzian distribution

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Abstract

Recommended

Traversable wormholes with exponential shape function in modified gravity and general relativity: A comparative study

Traversable wormhole models in modified theories of gravity

Yukawa–Casimir wormhole model in F(R,T) framework

Energy conditions of traversable wormhole in the deformed f(R) gravitational model

Traversable wormholes in Einsteinian-cubic-gravity with hybrid shape functions

Traversable wormhole solutions in f(R,T) gravity with noncommutative geometry

Traversable wormhole solutions with non-exotic fluid in framework of f(Q) gravity

Two different shape functions for wormholes in f(R) theory with non-commutative geometry and Lorentzian distribution

Yukawa–Casimir wormhole model in $F (R, T)$ framework

Energy conditions of traversable wormhole in the deformed $f (R)$ gravitational model

Traversable wormhole solutions in $f (R, T)$ gravity with noncommutative geometry

Traversable wormhole solutions with non-exotic fluid in framework of $f (Q)$ gravity

Two different shape functions for wormholes in $f (R)$ theory with non-commutative geometry and Lorentzian distribution