It is well known that $d=2N+1$ dimensional pure Lovelock metrics do not describe bounded distributions neither do they admit nontrivial vacuum solutions. On this basis it has been variously claimed that matter fields should be nondynamical. However, from earlier work it has long been demonstrated fairly generally that $2N+1$ pure Lovelock solutions are not kinematic. In this work we find perfect fluid filled universes with $d=2N+1$ that exhibit curvature of spacetime. New classes of exact solutions for pure Gauss–Bonnet gravity ($N=2$) are generated by integrating the pressure isotropy condition with suitable metric potential choices for the critical spacetime dimension 5. Amongst the physically important cases we study are the Vaidya–Tikekar superdense star ansatz, the Finch–Skea model as well as isothermal fluids. The physical properties are analysed with the aid of graphical plots and the model is found to be causal and stable in the sense of Chandrasekhar and satisfies the energy conditions. Finally we examine the most general Lovelock polynomials for all $N$ and $d=2N+1$. In particular the special case $N=3$, $d=7$ has not been considered previously in the literature and we discover a number of classes of exact solutions for this case.

众所周知 $d=2ñ+\mathrm{1个}$维度纯Lovelock度量标准不描述有界分布，也没有接受非平凡的真空解。在此基础上，已经有各种主张，物质场应该是非动力学的。但是，从较早的工作来看，长期以来一直相当普遍地证明$2ñ+\mathrm{1个}$纯粹的Lovelock解决方案不是运动学的。在这项工作中，我们找到了完美的充满流体的宇宙$d=2ñ+\mathrm{1个}$表现出时空弯曲。新的纯高斯-贝内特重力精确解类（$ñ=2$）是通过将压力各向同性条件与关键时空维度5的合适度量潜在选择进行集成而生成的。在我们研究的物理上重要的案例中，包括Vaidya–Tikekar超稠密星型ansatz，Finch–Skea模型以及等温流体。借助图形绘图分析了物理性质，发现该模型在钱德拉塞卡（Chandrasekhar）的意义上是因果关系且稳定的，并且满足能源条件。最后，我们检查所有的最一般的Lovelock多项式$ñ$ 和 $d=2ñ+\mathrm{1个}$。特别是特殊情况$ñ=3$， $d=7$ 文献中以前没有考虑过这种情况，因此我们发现了许多此类情况的精确解。