A new class of solutions describing analytical solutions for compact stellar structures has been developed within the tenets of General Relativity. Considering the inherent anisotropy in compact stars, a stable and causal model for realistic anisotropic neutron stars was obtained using the general theory of relativity. Assuming a physically acceptable nonsingular form of one metric potential and radial pressure containing the curvature parameter R, the constant k and the radius r, analytical solutions to Einstein’s field equations for anisotropic matter distribution were obtained. Taking the value of k as −0.44, it was found that the proposed model obeys all necessary physical conditions, and it is potentially stable and realistic. The model also exhibits a linear equation of state, which can be applied to describe compact stars.

中文翻译：

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广义相对论中描述各向异性中子星的一类新解析解

在广义相对论的原则下，已经开发了一类描述致密恒星结构解析解的新解。考虑致密星固有的各向异性，利用广义相对论得到了现实各向异性中子星的稳定因果模型。假设一个包含曲率参数的度量势和径向压力的物理上可接受的非奇异形式R, 常数ķ和半径r，得到了爱因斯坦场方程各向异性物质分布的解析解。取值ķ为-0.44，发现所提出的模型服从所有必要的物理条件，并且具有潜在的稳定性和现实性。该模型还展示了一个线性状态方程，可用于描述致密恒星。