Abstract
We study Morris–Thorne static traversable wormhole solutions in different modified theories of gravity. We focus our study on the quadratic gravity f({mathscr {R}}) = {mathscr {R}}+a{mathscr {R}}^2, power-law f({mathscr {R}}) = f_0{mathscr {R}}^n, log-corrected f({mathscr {R}})={mathscr {R}}+alpha {mathscr {R}}^2+beta {mathscr {R}}^2ln beta {mathscr {R}} theories, and finally on the exponential hybrid metric-Palatini gravity 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=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.
Highlights
In Figure. 1 one can see the Penrose diagram, where i0 is the infinitely far spacelike point, i− is the infinitely distant past, i+ is the infinitely distant future point
We investigate the null energy condition, the weak energy condition, and the strong energy condition with the suitable shape function b(r )
In GR wormholes are supported by exotic matter, which involves a stress-energy tensor that violates the null energy condition (NEC) [27,31,51]
Summary
In Figure. 1 one can see the Penrose diagram, where i0 is the infinitely far spacelike point, i− is the infinitely distant past, i+ is the infinitely distant future point. H + is the black hole horizon and H − is the white hole antihorizon, is a spacelike geodesic trajectory through both universes (Cauchy surface). One of the first wormhole options, and at the moment one of the most plausible, is the option proposed by [31] This is the static traversable Morris-Throne wormhole. This type of wormhole can connect two points of spacetime, and its throat is located in the bulk (with dbulk > 4). There exists a conformal transformation that connects the two theories
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