On the existence and stability of traversable wormhole solutions in modified theories of gravity

Oleksii Sokoliuk; Alexander Baransky

doi:10.1140/epjc/s10052-021-09560-4

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2021) 81: 781
https://doi.org/10.1140/epjc/s10052-021-09560-4

Regular Article - Theoretical Physics

On the existence and stability of traversable wormhole solutions in modified theories of gravity

Oleksii Sokoliuk¹^,2^a and Alexander Baransky¹

¹ Astronomical Observatory, Taras Shevchenko National University of Kyiv, 3 Observatorna St., 04053, Kyiv, Ukraine
² Astronomical Observatory of the National Academy of Sciences of Ukraine (MAO NASU), 03143, Kyiv, Ukraine

^a oleksii.sokoliuk@mao.kiev.ua

Received: 24 May 2021
Accepted: 18 August 2021
Published online: 31 August 2021

Abstract

We study Morris–Thorne static traversable wormhole solutions in different modified theories of gravity. We focus our study on the quadratic gravity $f (R) = R + a R^{2}$ $f({\mathscr {R}}) = {\mathscr {R}}+a{\mathscr {R}}^2$ , power-law $f (R) = f_{0} R^{n}$ $f({\mathscr {R}}) = f_0{\mathscr {R}}^n$ , log-corrected $f (R) = R + α R^{2} + β R^{2} ln β R$ $f({\mathscr {R}})={\mathscr {R}}+\alpha {\mathscr {R}}^2+\beta {\mathscr {R}}^2\ln \beta {\mathscr {R}}$ theories, and finally on the exponential hybrid metric-Palatini gravity $f (\hat{R}) = ζ (1 + e^{- \frac{\hat{R}}{Φ}})$ $f(\mathscr {\hat{R}})=\zeta \bigg (1+e^{-\frac{\hat{{\mathscr {R}}}}{\varPhi }}\bigg )$ . Wormhole fluid near the throat is adopted to be anisotropic, and redshift factor to have a constant value. We solve numerically the Einstein field equations and we derive the suitable shape function for each MOG of our consideration by applying the equation of state $p_{t} = ω ρ$ $p_t=\omega \rho$ . Furthermore, we investigate the null energy condition, the weak energy condition, and the strong energy condition with the suitable shape function b(r). The stability of Morris–Thorne traversable wormholes in different modified gravity theories is also analyzed in our paper with a modified Tolman–Oppenheimer–Voklov equation. Besides, we have derived general formulas for the extra force that is present in MTOV due to the non-conserved stress-energy tensor.

© The Author(s) 2021

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