We work out the junction conditions for $f(R)$ gravity formulated in metric-affine (Palatini) spaces using a tensor distributional approach. These conditions are needed for building consistent models of gravitating bodies with an interior and exterior regions matched at some hypersurface. Some of these conditions depart from the standard Darmois-Israel ones of General Relativity and from their metric $f(R)$ counterparts. In particular, we find that the trace of the stress-energy momentum tensor in the bulk must be continuous across the matching hypersurface, though its normal derivative need not to. We illustrate the relevance of these conditions by considering the properties of stellar surfaces in polytropic models, showing that the range of equations of state with potentially pathological effects is shifted beyond the domain of physical interest. This confirms, in particular, that neutron stars and white dwarfs can be safely modelled within the Palatini $f(R)$ framework.

中文翻译：

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Palatini f(R) 重力中的连接条件

我们使用张量分布方法计算出在度量仿射（Palatini）空间中制定的 $f(R)$ 重力的连接条件。需要这些条件来构建具有在某些超曲面上匹配的内部和外部区域的引力体的一致模型。其中一些条件与广义相对论的标准 Darmois-Israel 条件以及它们的度量 $f(R)$ 对应物不同。特别是，我们发现体中应力-能量动量张量的迹线在匹配的超曲面上必须是连续的，尽管其法向导数不需要。我们通过考虑多方模型中恒星表面的特性来说明这些条件的相关性，表明具有潜在病理影响的状态方程的范围超出了物理兴趣的范围。