The main focus of this paper is to explore the possibility of providing a new family of exact solutions for suitable anisotropic spherically symmetric systems in the realm of general relativity involving the embedding spherically symmetric static metric into the five-dimensional pseudo-Euclidean space. In this regard, we ansatz a new metric potential \(\lambda (r)\), and we obtained the other metric potential \(\nu (r)\) by mains of embedding class one approach. The unknown constants are determined by the matching of interior space-time with the Schwarzschild exterior space-time. The physical acceptability of the generating celestial model for anisotropic compact stars is approved via acting several physical tests of the main salient features viz., energy density, radial and tangential pressures, anisotropy effect, dynamical equilibrium, energy conditions, and dynamical stability, which are well-compared with experimental statistics of four different compact stars: PSR J1416-2230, PSR J1903+327, 4U 1820-30 and Cen X-3. Conclusively, all the compact stars under observations are realistic, stable, and are free from any physical or geometrical singularities. We find that the embedding class one solution for anisotropic compact stars is viable and stable, plus, it provides circumstantial evidence in favor of super-massive pulsars.

本文的主要重点是探索在广义相对论领域中为合适的各向异性球对称系统提供一系列新的精确解的可能性，其中涉及将球对称静态度量嵌入到五维拟欧几里德空间中。在这方面，我们解析了一个新的度量电势\（\ lambda（r）\），并获得了另一个度量电势\（\ nu（r）\）通过嵌入第一类方法的要领。未知常数由内部时空与Schwarzschild外部时空的匹配确定。通过对主要突出特征进行几次物理测试，即能量密度，径向和切向压力，各向异性效应，动态平衡，能量条件和动态稳定性，对生成的天体模型进行各向异性物理恒星的物理可接受性得到了认可。与四个不同的紧凑型恒星的实验统计数据相比要好得多：PSR J1416-2230，PSR J1903 + 327、4U 1820-30和Cen X-3。结论是，观测中的所有紧凑恒星都是真实的，稳定的，并且没有任何物理或几何奇异点。我们发现，各向异性紧凑星的嵌入第一类解决方案是可行且稳定的，此外，