Validity of energy conditions of matter in traversable wormholes under the $f(Q)$ modified gravity theory

Abstract: In the framework of the theory of general relativity, in order to obtain stable traversable wormholes, matter needs to violate the null energy condition. It is well known that the violation of the energy condition (EC) of matter leads to various physical problems. To address this issue, researchers have turned their attention to exploring modified theories of gravity, aiming to avoid the violation of ECs by introducing geometric terms. In this paper, within the framework of the $f(Q)$ modified gravitational theory, we investigate the effectiveness of ECs for matter in traversable wormholes. We examine the compliance of four types of energy conditions (weak energy condition, null energy condition, dominant energy condition, and strong energy condition) in the model by selecting a power-law model for $f(Q)$ and considering different shape functions $b(r)$. Our study reveals that for traversable wormholes realized through the $f(Q)$ modified gravity theory using the power-law model $f(Q)=a(-Q)^n$, all four types of ECs for matter can be satisfied. There is no need to introduce exotic matter (violating the null energy condition) or special matter (violating other energy conditions) artificially in the physics of wormholes.