标题： 在$f\left(R,T^2\right)$引力中满足能量条件的虫洞几何结构 显示英文标题

标题： Wormhole geometries in $f\left(R,T^2\right)$ gravity satisfying the energy conditions

摘要： 我们探讨了在能量动量平方引力框架下可穿越虫洞时空的性质，也称为$f(R,T^2)$引力，在此框架中，$R$表示里奇标量，$T_{ab}$是能量动量张量，$T^2 = T_{ab}T^{ab}$。 采用线性泛函形式$f(R,T^2) = R + \gamma T^2$，我们证明了存在满足所有能量条件而无需精细调节模型参数的广泛虫洞解。 由于场方程的固有复杂性，这些解是通过分析递归方法构建的。 然而，它们缺乏自然定位，需要与外部真空区域连接。 为了解决这个问题，我们推导出相应的连接条件，并确定匹配必须始终是平滑的，从而排除了在界面处形成薄壳的可能性。 使用这些条件，我们将内部虫洞几何与外部施瓦茨希尔德解匹配，得到满足整个时空所有能量条件的局部化、静态和球对称虫洞。 最后，我们将分析扩展到对$T^2$更复杂的依赖关系，证明只要不引入$R$和$T^2$之间的混合项，该方法仍然适用。 显示英文摘要

摘要： We explore the properties of traversable wormhole spacetimes within the framework of energy-momentum squared gravity, also known as $f(R,T^2)$ gravity, where $R$ represents the Ricci scalar, $T_{ab}$ is the energy-momentum tensor, and $T^2 = T_{ab}T^{ab}$. Adopting a linear functional form $f(R,T^2) = R + \gamma T^2$, we demonstrate the existence of a wide range of wormhole solutions that satisfy all of the energy conditions without requiring fine-tuning of the model parameters. Due to the inherent complexity of the field equations, these solutions are constructed through an analytical recursive method. However, they lack a natural localization, requiring a junction with an external vacuum region. To address this, we derive the corresponding junction conditions and establish that the matching must always be smooth, precluding the formation of thin shells at the interface. Using these conditions, we match the interior wormhole geometry to an exterior Schwarzschild solution, yielding localized, static, and spherically symmetric wormholes that satisfy all the energy conditions throughout the entire spacetime. Finally, we extend our analysis to more intricate dependencies on $T^2$, demonstrating that the methodology remains applicable as long as no mixed terms between $R$ and $T^2$ are introduced.