Non-exotic asymptotically flat wormholes in $f(Q,T)$ gravity

TL;DR

This work probes the existence of traversable wormholes in the extended $f(Q,T)$ gravity framework, focusing on a linear model $f(Q,T)=\alpha Q+\beta T$ with a zero-redshift function. By deriving the modified field equations for an anisotropic fluid, it shows that the effective energy conditions can be satisfied in $f(Q,T)$ gravity when the coupling parameter $\gamma(\alpha,\beta)=\alpha/(1+\beta)$ is negative, even if GR would require exotic matter. The authors obtain explicit solutions: (i) a power-law shape function $b(r)=r^{n(\omega,\beta)}$ from a linear EoS $p=\omega\rho$, and (ii) asymptotically linear EoS leading to an integral expression for $b(r)$, with concrete shape functions that realize non-exotic wormholes under suitable parameter choices. Overall, the study demonstrates that nonmetricity–matter coupling in $f(Q,T)$ gravity can sustain traversable wormholes without exotic matter in a broad parameter regime, offering new insights into wormhole topology beyond GR.

Abstract

In this study, we investigate the possible existence of static and spherically symmetric wormhole solutions within the context of the newly formulated extended $f(Q,T)$ gravity. We analyze a linear model, $f(Q,T)=αQ+ βT$, and focus on traversable wormholes. By applying the variational method, we derive modified versions of the field equations that are influenced by an anisotropic matter source for a zero redshift function. It has been observed that the violation of energy conditions is influenced by the parameters $α$ and $β$. We reach the conclusion that solutions which violate the radial and lateral null energy condition in the context of general relativity may still adhere to the energy conditions within the realm of $f(Q,T)$ gravity. To begin with, by utilizing a linear equation of state for radial pressure, we obtain a power-law shape function. Additionally, we investigate solutions defined by a variable equation of state parameter. A broad spectrum of non-exotic wormhole solutions has been identified, contingent upon the particular parameters of the model.

Figures (6)

• Figure 1: The graph depicts the correlation between $n(\omega, \beta)$ and the variables $\omega$ and $\beta$. It is clear that $n(\omega, \beta)$ is positive within a certain range of $\alpha$ and $m$ (a, b) , , while $n$ is negative in some different ranges (c, d).
• Figure 2: The graph depicts the functions $H(r)$(red), $H_1(r)$(green), $H_2(r)$(yellow), $H_3(r)$(blue), and $H_4(r)$(violet) plotted against the radial coordinate for the shape function $b(r)=\left(\frac{2}{r+1}\right)^4$ within the framework of $f(Q, T)$. It is evident that all ECs, except for the DEC, are satisfied. See the text for details.
• Figure 3: The graph depicts the functions $H(r)$(red), $H_1(r)$(green), $H_2(r)$(yellow), $H_3(r)$(blue), and $H_4(r)$(violet) plotted against the radial coordinate for the shape function $b(r)=\exp(\frac{1-r^4}{2})$ within the framework of $f(Q, T)$. It is evident that all ECs, except for the DEC, are satisfied. See the text for details.
• Figure 4: The graph depicts the functions $H(r)$(red), $H_1(r)=H_3(r)$(green), $H_2(r)$(yellow), and $H_4(r)$(violet) plotted against the radial coordinate for the shape function $b(r)=\left(\frac{33}{23r+10}\right)^{\frac{12}{23}}$ within the framework of $f(Q, T)$. It is evident that all ECs are violated. See the text for details.
• Figure 5: The graph depicts the functions $H(r)$(red), $H_1(r)=H_3(r)$(green), $H_2(r)$(yellow), and $H_4(r)$(violet) plotted against the radial coordinate for the shape function $b(r)=\left(\frac{18}{10r+8}\right)^{\frac{9}{5}}$ within the framework of $f(Q, T)$. It is evident that all ECs, except for the DEC, are satisfied. See the text for details.