The Palatini [Formula: see text] gravity theory is considered. The standard Einstein–Hilbert action is replaced by an arbitrary function of the Ricci scalar [Formula: see text] and of the trace [Formula: see text] of the energy-momentum tensor. In the Palatini approach, the Ricci scalar is a function of the metric and the connection. These two quantities, metric and connection, are taken as independent variables. Then, it is examined whether Palatini [Formula: see text] gravity theory allows solutions in which lead to violation of causality. The Gödel and Gödel-type spacetimes are considered. In addition, a critical radius, which permits to examine limits for violation of causality, is calculated. It is shown that, for different matter contents, noncausal solutions can be avoided in this Palatini gravitational theory.

中文翻译：

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Palatini f(R,T) 引力理论中的 Gödel 和 Gödel 型解

考虑了帕拉蒂尼[公式：见正文]引力理论。标准的 Einstein-Hilbert 作用被 Ricci 标量 [公式：见正文] 和能量-动量张量的迹 [公式：见正文] 的任意函数代替。在 Palatini 方法中，Ricci 标量是度量和连接的函数。这两个量，度量和连接，被视为自变量。然后，检查Palatini [公式：见正文] 引力理论是否允许导致违反因果关系的解决方案。考虑了哥德尔和哥德尔型时空。此外，计算允许检查违反因果关系的极限的临界半径。结果表明，对于不同的物质含量，帕拉蒂尼引力理论可以避免非因果解。