Non-exotic traversable wormhole solutions in linear fleft( R,Tright) gravity

Abstract

In this work we analyze traversable wormhole solutions in the linear form of fleft( R,Tright) =R+lambda T gravity satisfying the Null, Weak, Strong, and Dominant Energy Conditions (NEC, WEC, SEC, and DEC respectively) for the entire spacetime. These solutions are obtained via a fully analytical parameter space analysis of the free parameters of the wormhole model, namely the exponents controlling the degree of the redshift and shape functions, the radius of the wormhole throat r_0, the value of the redshift function at the throat zeta _0, and the coupling parameter lambda . Bounds on these free parameters for which the energy conditions are satisfied for the entire spacetime are deduced and two explicit solutions are provided. Even if some of these bounds are violated, leading to the violation of the NEC at some critical radius r_c>r_0, it is still possible to find physically relevant wormhole solutions via a matching with an exterior vacuum spacetime in the region where the energy conditions are still satisfied. For this purpose, we deduce the set of junction conditions for the form of fleft( R,Tright) considered and provide an explicit example. These results seem to indicate that a wide variety of non-exotic wormhole solutions are attainable in the fleft( R,Tright) theory without the requirement of fine-tuning.