It is indeed remarkable that while charged anisotropic models with the embedding class one property are abundant, there are no reports of the physically important isotropic case despite its simplicity. In fact, the Karmarkar condition turns out to be the only avenue to generate all such stellar models algorithmically. The process of determining exact solutions is almost trivial: either specify the spatial potential and perform a single integration to obtain the temporal potential or simply select any temporal potential and get the space potential without any integrations. Then the model is completely determined and all dynamical quantities may be calculated. The difficulty lies in ascertaining whether such models satisfy elementary physical requisites. A number of physically relevant models are considered though not exhaustively. We prove that conformally flat charged isotropic stars of embedding class one do not exist. If spacetime admits conformal symmetries then the space potential must be of the Finch–Skea type in this context. A general metric ansatz is stated which contains interesting special cases. The Finch–Skea special case is shown to be consistent with the expectations of a stellar model while the Vaidya–Tikekar special case generates a physically viable cosmological fluid. The case of an isothermal sphere with charge and the Karmarkar property is examined and is shown to be defective. When the Karmarkar property is abandoned for isothermal charged fluids, the spacetimes are necessarily flat.

确实值得注意的是，尽管具有嵌入一类性质的带电各向异性模型非常丰富，但尽管简单，却没有关于物理上重要的各向同性情况的报道。实际上，Karmarkar条件原来是通过算法生成所有此类恒星模型的唯一途径。确定精确解的过程几乎是微不足道的：要么指定空间势并执行单个积分以获得时间势，要么简单地选择任何时间势并获得空间势而不进行任何积分。然后，完全确定模型并计算所有动力学量。困难在于确定此类模型是否满足基本的物理要求。尽管不详尽，但仍考虑了许多与物理相关的模型。我们证明不存在嵌入第一类的保形的带电各向同性恒星。如果时空允许共形对称，则在这种情况下，空间势必须为Finch–Skea类型。说明了一个通用度量标准ansatz，其中包含有趣的特殊情况。Finch–Skea特例显示出与恒星模型的期望一致，而Vaidya–Tikekar特例生成了物理上可行的宇宙流体。研究了带电荷和Karmarkar性质的等温球体的情况，发现这种情况是有缺陷的。当Karmarkar属性被等温带电流体抛弃时，时空必定是平坦的。如果时空允许共形对称，则在这种情况下，空间势必须为Finch–Skea类型。说明了一个通用度量标准ansatz，其中包含有趣的特殊情况。Finch–Skea特例显示出与恒星模型的期望一致，而Vaidya–Tikekar特例生成了物理上可行的宇宙流体。研究了带电荷和Karmarkar性质的等温球体的情况，发现这种情况是有缺陷的。当Karmarkar属性被等温带电流体抛弃时，时空必定是平坦的。如果时空允许共形对称，则在这种情况下，空间势必须为Finch–Skea类型。说明了一个通用度量标准ansatz，其中包含有趣的特殊情况。Finch–Skea特例显示出与恒星模型的期望一致，而Vaidya–Tikekar特例生成了物理上可行的宇宙流体。研究了带电荷和Karmarkar性质的等温球体的情况，发现这种情况是有缺陷的。当Karmarkar属性被等温带电流体抛弃时，时空必定是平坦的。Finch–Skea特例显示出与恒星模型的期望一致，而Vaidya–Tikekar特例生成了物理上可行的宇宙流体。研究了带电荷和Karmarkar性质的等温球体的情况，发现这种情况是有缺陷的。当Karmarkar属性被等温带电流体抛弃时，时空必定是平坦的。Finch–Skea特例显示出与恒星模型的期望一致，而Vaidya–Tikekar特例生成了物理上可行的宇宙流体。研究了带电荷和Karmarkar性质的等温球体的情况，发现这种情况是有缺陷的。当Karmarkar属性被等温带电流体抛弃时，时空必定是平坦的。