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

Abstract

We study Morris–Thorne static traversable wormhole solutions in different modified theories of gravity. We focus our study on the quadratic gravity $$f({\mathscr {R}}) = {\mathscr {R}}+a{\mathscr {R}}^2$$ 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.

Probing the existence of the ZTF Casimir wormholes in the framework of $f(\mathcal{R})$ gravity

“…Now, we think that it will be appropriate to compare our results for ZTF Casimir wormhole with the usual Morris-Thorne wormholes within the same f (R) theories of gravity considered. Morris-Thorne wormholes were investigated in details within the both quadratic and power-law gravities in the work [42]. In the quadratic gravity, it was shown that NEC, SEC for radial and tangential pressures were respected only for α ≥ 0 and only in the case, when α is relatively small (which coincides well with the Casimir wormholes, that was investigated in the present study).…”

“…Casimir Energy is currently the only possible substitute for exotic matter, that could be obtained in the laboratory. Firstly, we could present energy conditions, that we will use in this paper [42]:…”

“…where L M is the Lagrangian of the matter fields. Then, by varying the Einstein-Hilbert action we could obtain (modified) EFE [42]:…”

Yang-Mills Casimir wormholes in D = 2 + 1

“…The stability of compact objects, such as stellar structures, can be also examined through the Tolman-Oppenheimer-Volkov (TOV) equation, initially introduced in the context of neutron stars [39,40]. Hence, the stability conditions for wormholes could be investigated by employing an equilibrium condition obtained from the TOV equation [41][42][43][44]. Combining the Morris-Thorne metric ansatz (2.2) with the conservation law of stress-energy tensor ∇ µ T µν = 0, we obtain the following TOV equation in a 2 + 1 dimensional spacetime:…”

A study of wormhole geometries in symmetric teleparallel gravity

“…Here, a specific logarithmic corrected f (Q) type function is considered, which is defined as [30,31]…”