Wormhole geometries in $f(Q)$ gravity and the energy conditions

TL;DR

This paper explores wormhole solutions within $f(Q)$ gravity, demonstrating conditions under which such geometries can exist and violate energy conditions, with specific models and constraints analyzed.

Contribution

It systematically studies wormhole solutions in $f(Q)$ gravity, highlighting the impact of different $f(Q)$ forms and shape functions on energy condition violations.

Findings

Wormhole solutions violate null energy conditions near the throat.

No solutions exist for the specific form $f(Q)= Q+ eta Q^2$.

Exact models can have $ ho geq 0$ while violating energy conditions.

Abstract

Following the recent theory of $f(Q)$ gravity, we continue to investigate the possible existence of wormhole geometries, where $Q$ is the non-metricity scalar. Recently, the non-metricity scalar and the corresponding field equations have been studied for some spherically symmetric configurations in [ Phys. Lett. B 821, 136612 (2021) and Phys. Rev. D 103, 124001 (2021) ]. One can note that field equations are different in these two studies. Following [Phys. Rev. D 103, 124001 (2021)], we systematically study the field equations for wormhole solutions and found the violation of null energy conditions in the throat neighborhood. More specifically, considering specific choices for the $f(Q)$ form and for constant redshift with different shape functions, we present a class of solutions for static and spherically symmetric wormholes. Our survey indicates that wormhole solutions could not exist for specific form function $f(Q)= Q+ \alpha Q^2$. To summarize, exact wormhole models can be constructed with violation of the null energy condition throughout the spacetime while being $\rho \geq 0$ and vice versa.