Nonminimal curvature–matter coupled wormholes with matter satisfying the null energy condition

Abstract\nRecently, exact solutions of wormhole geometries supported by a nonminimal curvature-matter coupling were found, where the nonminimal coupling minimizes the violation of the null energy condition of normal matter at the throat. In this brief report, we present a solution where normal matter satisfies the energy conditions at the throat and it is the higher order curvature derivatives of the nonminimal coupling that is responsible for the null energy condition violation, and consequently for supporting the respective wormhole geometries. For simplicity, we consider a linear R nonmiminal curvature-matter coupling and an explicit monotonically increasing function for the energy density. Thus, the solution found is not asymptotically flat, but may in principle be matched to an exterior vacuum solution. Introduction: Recently, f (R) modified theories of gravity have received a great deal of attention [ 1 ], in particular , to account for the late-time cosmic acceleration [ 2 ]. An interesting generalization of f (R) gravity involves the inclusion of an explicit coupling between the curvature scalar and matter [ 3 ]. The latter coupling imposes the nonconservation of the stress-energy tensor, and consequently implies nongeodesic motion [ 3 ]. The action for a nonminimal curvature-matter coupling in f (R) modified theories of gravity, considered in this work [ 3 ], is given by

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