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 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+ alpha Q^2. To summarize, exact wormhole models can be constructed with violation of the null energy condition throughout the spacetime while being rho ge 0 and vice versa.
Highlights
It is well known in general relativity that wormhole spacetimes are supported by exotic matter whose stress– energy tensor violates the null energy condition (NEC) [3,5], according to the needs of the geometrical structure
In the present manuscript our interest is to find exact and correct field equations in f (Q) gravity for static and spherical symmetric configuration. We further extend this analysis and find an exact wormhole solution, where we showed the violation of the NEC of normal matter at the throat of the wormhole
We have explored wormhole geometries in the framework of f (Q) gravity for static and spherically symmetric spacetime
Summary
It is well known in general relativity that wormhole spacetimes are supported by exotic matter whose stress– energy tensor violates the null energy condition (NEC) [3,5], according to the needs of the geometrical structure. In the present manuscript our interest is to find exact and correct field equations in f (Q) gravity for static and spherical symmetric configuration We further extend this analysis and find an exact wormhole solution, where we showed the violation of the NEC of normal matter at the throat of the wormhole. 2 we give an overview about the f (Q) gravity, and we find the corresponding field equations for static and spherically symmetric spacetime in Sect. With the formalism of f (Q) gravity specified, the conservation of the energy momentum tensor is ensured by the field equations In this discussion our main interest is to formulate the gravitational field equations governing static and spherically symmetric spacetimes of (7) to the study of wormhole geometries
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