We present the features of a model which generalizes Schwarzschild’s homogeneous star by adding a transition zone for the density near the surface. By numerically integrating the modified TOV equations for the \(f(\mathcal {R})=\mathcal {R}+\lambda \mathcal {R}^2\) Palatini theory, it is shown that the ensuing configurations are everywhere finite. Depending on the values of the relevant parameters, objects more, less or as compact as those obtained in GR with the same density profile have been shown to exist. In particular, in some region of the parameter space the compactness is close to that set by the Buchdahl limit.

我们介绍了模型的特征，该模型通过为表面附近的密度添加过渡带来概括Schwarzschild的均质恒星。通过对\（f（\ mathcal {R}）= \ mathcal {R} + \ lambda \ mathcal {R} ^ 2 \） Palatini理论的数值修正积分进行数值积分，可以证明随之而来的结构无处不在。取决于相关参数的值，已显示存在与GR中具有相同密度分布的对象更多，更少或紧凑的对象。特别是，在参数空间的某些区域中，紧密度接近由布赫达尔极限设置的紧密度。