We present here a new class of singularity free interior solutions relevant for the description of realistic anisotropic compact stellar objects with spherically symmetric matter distribution. In this geometric approach, specific choices of one of the metric functions and a selective anisotropic profile allow us to develop a stellar model by solving Einstein Field equations. The interior solutions thus obtained are matched with the Schwarzschild exterior metric over the bounding surface of a compact star. These matching conditions together with the condition that the radial pressure vanishes at the boundary are used to fix the model parameters. The different physical features for the developed model explicitly studied from the aspect of the pulsar 4U\(1820-30\) with its current estimated data (mass \(=1.46 \pm 0.21~M\odot \) and radius \(=11.1 \pm 1.8\) km (Özel et al.: ApJ 820(1): 28, 2016) ). Analysis has shown that all the physical aspects are acceptable demanded for a physically admissible star and satisfy all the required physical conditions. The stability of the model is also explored in the context of causality conditions, adiabatic index, generalized Tolman–Oppenheimer–Volkov (TOV) equation, Buchdahl Condition and Herrera Cracking Method. To show that the developed model is compatible with a wide range of recently observed pulsars, various relevant physical variables are also highlighted in tabular form. The data studied here are in agreement with the observation of gravitational waves from the first binary merger event. Assuming a particular surface density (\(7.5 \times 10^{14}\text { gm cm}^{-3}\)), the mass-radius (\(M - b\)) relationship and the radius-central density relationship (\(b - \rho (0)\)) of the compact stellar object are analyzed for this model. Additionally, comparing the results with a slow rotating configuration, we have also discussed moment of inertia and the time period using Bejger-Haensel idea.

我们在这里提出了一类新的无奇异内部解，与具有球形对称物质分布的现实各向异性紧凑恒星物体的描述有关。在这种几何方法中，度量函数之一的特定选择和各向异性各向异性的选择使我们能够通过求解爱因斯坦场方程来建立恒星模型。这样获得的内部解在紧凑恒星的边界表面上与Schwarzschild外部度量相匹配。这些匹配条件与径向压力在边界处消失的条件一起用于固定模型参数。从脉冲星4U \（1820-30 \）方面，以当前估计数据（质量）明确研究了已开发模型的不同物理特征。\（= 1.46 \ pm  0.21〜M \ odot \）和半径\（= 11.1 \ pm 1.8 \） km（Özelet al .: ApJ 820（1）：28，2016））。分析表明，对于物理上可接受的恒星，所有物理方面都是可接受的要求，并且满足所有必需的物理条件。在因果条件，绝热指数，广义Tolman–Oppenheimer–Volkov（TOV）方程，Buchdahl条件和Herrera破裂方法的背景下，也研究了模型的稳定性。为了表明开发的模型与最近观测到的各种脉冲星兼容，还以表格形式突出了各种相关的物理变量。此处研究的数据与第一次二进制合并事件产生的引力波一致。假设特定的表面密度（\（7.5 \ times 10 ^ {14} \ text {gm cm} ^ {-3} \）），质量半径（\（M-b \））关系和半径-中心密度关系（\（b -针对此模型分析了紧凑型恒星对象的\ rho（0）\））。此外，通过将结果与慢速旋转配置进行比较，我们还使用Bejger-Haensel思想讨论了惯性矩和时间段。