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We study Morris–Thorne static traversable wormhole solutions in different modified theories of gravity. We focus our study on the quadratic gravity    $$f({\mathscr {R}}) = {\mathscr {R}}+a{\mathscr {R}}^2$$  f ( R ) = R + a R 2 , power-law    $$f({\mathscr {R}}) = f_0{\mathscr {R}}^n$$  f ( R ) = f 0 R n , log-corrected    $$f({\mathscr {R}})={\mathscr {R}}+\alpha {\mathscr {R}}^2+\beta {\mathscr {R}}^2\ln \beta {\mathscr {R}}$$  f ( R ) = R + α R 2 + β R 2 ln β R theories, and finally on the exponential hybrid metric-Palatini gravity    $$f(\mathscr {\hat{R}})=\zeta \bigg (1+e^{-\frac{\hat{{\mathscr {R}}}}{\varPhi }}\bigg )$$  f ( R ^ ) = ζ ( 1 + e - R ^ Φ ) . 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    $$p_t=\omega \rho $$  p t = ω ρ . 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.

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