Traversable Wormholes with Non-Exotic Matter: The Role of Higher Curvature Corrections

Abstract

In this paper, we explore wormhole solutions in a higher-derivative theory of gravity where the action depends not only on the Ricci scalar $R$, but also on its d'Alembertian, $\Box R$. Such $f(R,\Box R)$ models are motivated by quantum corrections to general relativity and naturally extend the space of possible gravitational geometries. Our goal is to examine whether traversable wormholes can exist in this framework and to understand the role of higher-order curvature terms in supporting them. We derive the field equations for a static, spherically symmetric wormhole and study their solutions using both analytical arguments and numerical methods. Particular attention is given to the classical energy conditions, which are usually violated in wormhole physics. We find that the higher-derivative corrections can effectively contribute to the stress-energy tensor, reducing the amount of exotic matter required at the throat, and in some cases eliminating the need for it altogether.