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Wormhole solutions for different shape functions in 4D Einstein Gauss–Bonnet gravity

Riaz Ahmed

https://orcid.org/0000-0003-0840-335X

University of Central Punjab Lahore, Lahore, Pakistan

E-mail Address: ahmedoriya@gmail.com

Corresponding author.

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G. Abbas

Department of Mathematics the Islamia University of Bahawalpur, Bahawalpur, Pakistan

E-mail Address: abbasg91@yahoo.com

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, and

Saira Arshad

University of Central Punjab Lahore, Lahore, Pakistan

E-mail Address: sairaarshad590@gmail.com

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https://doi.org/10.1142/S0219887822501092Cited by:4 (Source: Crossref)

Abstract

In this paper, we obtain an exact spherically symmetric wormhole solution with anisotropic matter distribution in the regularized four-dimensional (4D) Einstein Gauss–Bonnet gravity (4D EGB). Recently, a new attempt has been made to include nontrivial contributions of Gauss–Bonnet term to the gravitational dynamics by regularizing EGB gravity in $4$ $4$ -dimensions. To find the exact solution of the wormhole geometry, we studied two specific radial-dependent shape functions $b (r) = r_{0} {(\frac{cosh (r_{0})}{cosh (r)})}^{μ}$ $b (r) = r_{0} {(\frac{cosh (r_{0})}{cosh (r)})}^{μ}$ , $0 < μ < 1$ $0 < μ < 1$ and $b (r) = r_{0} (\frac{a^{r}}{a^{r_{0}}})$ $b (r) = r_{0} (\frac{a^{r}}{a^{r_{0}}})$ , $0 < a < 1$ $0 < a < 1$ in the context of 4D EGB gravity. For each shape function, we find the exact wormhole solution and analyze the properties of wormhole existence graphically. The anisotropic parameter, equation of state (EoS) and energy conditions are tested graphically for each shape function. The behavior of both shape functions is thoroughly evaluated with the throat radius $r = r_{0} = 1$ $r = r_{0} = 1$ . Specifically, we recovered the original results exactly to 4D Morris–Throne wormholes of General Relativity by simply imposing the limit as $α \to 0$ $α \to 0$ and comparison has been done between the branch results in 4D EGB gravity and General Relativity by graphical point of view.

Keywords:

AMSC: 37N20, 83C57, 83C56, 83E50, 83F05, 83E30, 83C05

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Vol. 19, No. 07

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Received 9 August 2021

Accepted 5 March 2022

Published: 7 April 2022

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Wormhole solutions for different shape functions in 4D Einstein Gauss–Bonnet gravity

Abstract

References

Existence of traversable wormholes with varied shape functions in $f (ℛ^{2}, 𝒯)$ gravity

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Wormhole solutions in $f (R, T) = R + α R^{2} + β ln T$ gravity

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

Wormhole modeling in R² gravity with linear trace term

Wormhole solutions in Rastall teleparallel gravity

Existence of wormholes in $f (𝒢)$ gravity using symmetries

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

Wormhole solutions for different shape functions in 4D Einstein Gauss–Bonnet gravity

Abstract

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