Abstract
In this paper, we study traversable wormholes in the context of f(R) gravity. Exact solutions of traversable wormholes are found by imposing the nonconstant Ricci scalar. These solutions asymptotically match spherical, flat and hyperbolic FRW metric. By choosing some static f(R) gravity models, we verify the standard energy conditions for the asymptotically spherical, flat and hyperbolic wormhole solutions. Unlike the Einstein gravity, we find that in the context of f(R) modified gravity, the asymptotically spherical, flat and hyperbolic wormhole solutions can respect the null energy condition (NEC) at the wormhole throat and near that. We find that in some static f(R) models, asymptotically flat and hyperbolic wormholes respect the weak energy condition (WEC) through the whole space.
Highlights
Traversable wormholes are throatlike geometrical structures which connect two separate and distinct regions of spacetimes and have no horizon or singularity
A fundamental ingredient in wormhole physics is the flaring-out condition of the throat, which in general relativity (GR) entails the violation of the null energy condition (NEC)
In the following we verify the null and weak energy condition for these asymptotically hyperbolic and spherical wormhole solutions in the background of static f (R) modified gravity models that we considered in the previous subsection
Summary
Traversable wormholes are throatlike geometrical structures which connect two separate and distinct regions of spacetimes and have no horizon or singularity. Lorentzian wormhole solutions were investigated in viable f(R) modified theories of gravity [51], which are consistent with observations of the solar system and cosmological evolution in [52,53,54,55,56,57] These wormholes were found in specific f(R) models which are considered to reproduce realistic scenarios of cosmological evolution based on the accelerated expansion of the universe. The existence of wormhole solutions in scalar–tensor and f (R) gravity was studied in [60,61] and it was shown that static wormhole solutions in these theories can be obtained with matter respecting the WEC when the effective gravitational constant is negative (which means the anti-gravitational property of the solutions) in some regions of space. The field equation (4) leads to the following relationships b r2
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