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

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 Mustafa (Phys Lett B 821:136612, 2021) and Lin and Zhai (Phys Rev D 103:124001, 2021). One can note that field equations are different in these two studies. Following Lin and Zhai (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+αQ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(Q)= Q+ \alpha Q^2$$\end{document}. To summarize, exact wormhole models can be constructed with violation of the null energy condition throughout the spacetime while being ρ≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho \ge 0$$\end{document} and vice versa.