We investigate the existence of inhomogeneous Szekeres spacetimes in Einstein-\ae ther theory. We show that inhomogeneous solutions which can be seen as extension of the Szekeres solutions existing in Einstein-\ae ther gravity only for a specific relation between the dimensionless coefficients which defines the coupling between the \ae ther filed with gravity. The two Szekeres classes of solutions are derived. Also a class of inhomogeneous FLRW-like spacetimes is allowed by the theory for arbitrary values of the dimensionless coefficients of the \ae ther field. The stability of the solutions obtained is performed from where we find that the field equations evolve more variously in Einstein-\ae ther than in General Relativity, where isotropic spacetimes and Kantowski-Sachs spacetimes are found to be attractors.

中文翻译：

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爱因斯坦-以太宇宙学中的非均匀时空

我们研究了爱因斯坦理论中不均匀 Szekeres 时空的存在。我们证明了非齐次解可以被看作是存在于爱因斯坦中的 Szekeres 解的扩展 -\ather 引力仅适用于无量纲系数之间的特定关系，该关系定义了 \ae 场与引力之间的耦合。派生了两个 Szekeres 类的解决方案。对于热场的无量纲系数的任意值，理论还允许一类不均匀的类 FLRW 时空。所得解的稳定性是从我们发现爱因斯坦场方程的演化比广义相对论更多样化的地方进行的，在广义相对论中，各向同性时空和康托夫斯基-萨克斯时空被发现是吸引子。