Abstract The aim of this paper is to explore a new parametric class of relativistic solutions to the Einstein field equations describing a spherically symmetric, static distribution of anisotropic fluid spheres to study the behavior of some of the cold stars in the setting of Karmarkar space-time continuum. We develop models of stellar objects for a range of parameter values of n and analyze their behavior through graphical representation. For each of these models, we have found that the metric potentials are well behaved inside the stellar interior and the physical parameters such as density, radial and tangential pressures, red-shift, radial speed, radial pressure density ratio and energy conditions display a continuous decrease from the center to surface of the stars whereas the mass, anisotropy, adiabatic indexes and compactification factor show a monotonous increase which imply that the proposed solution satisfy all the physical aspects of a realistic stellar objects. The stability of the solutions are verified by examining various stability aspects, viz., Zeldovich criteria, causality condition, Bondi condition, equilibrium condition (TOV-equation) and stable static criteria in connection to their cogency.

中文翻译：

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Karmarkar时空连续体中冷星的相对论参数嵌入I类解

摘要 本文的目的是探索描述各向异性流体球的球对称静态分布的爱因斯坦场方程的一类新的参数化相对论解，以研究一些冷星在卡马克时空背景下的行为。连续体。我们为一系列参数值 n 开发恒星物体模型，并通过图形表示分析它们的行为。对于这些模型中的每一个，我们发现度量势在恒星内部表现良好，并且诸如密度、径向和切向压力、红移、径向速度、径向压力密度比和能量条件等物理参数显示出连续的从恒星的中心到表面减少，而质量、各向异性、绝热指数和紧化因子显示单调增加，这意味着所提出的解决方案满足现实恒星物体的所有物理方面。解决方案的稳定性通过检查各种稳定性方面来验证，即 Zeldovich 标准、因果关系条件、Bondi 条件、平衡条件（TOV 方程）和与其说服力相关的稳定静态标准。