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arXiv · 2109.15105

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

Ayan Banerjee·Anirudh Pradhan·Takol Tangphati·Farook Rahaman
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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.

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Ayan Banerjee, Anirudh Pradhan, Takol Tangphati, Farook Rahaman. 2021-09-30. Wormhole geometries in $f(Q)$ gravity and the energy conditions. https://doi.org/10.1140/epjc%2Fs10052-021-09854-7

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