In the present work, we investigate the existence of compact star model in the background of gravity theory, where represents the Ricci scalar and refers to the energy-momentum tensor trace. Here, we use Karmarkar condition for the interior stellar setup so that a complete and precise model following the embedding class-I strategy can be obtained. For this purpose, we assume anisotropic matter contents along with static and spherically symmetric geometry of compact star. As Karmarkar embedding condition yields a relationship of metric potentials, therefore we assume a suitable form for one of the metric components as , where and represent constants and is a free parameter, and evaluate the other. We approximate the values of physical parameters like , and by utilizing the known values of mass and radius for the compact star Vela X-1. The validity of the acquired model is then explored for different values of coupling parameter graphically. It is found that the resulting solution is physically interesting and well-behaved.

中文翻译：

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基于重力的Karmarkar条件的通用嵌入I类模型

在目前的工作中，我们研究了紧凑星模型在背景下的存在。 重力理论，其中代表里奇标量，是指能量动量张量迹线。在这里，我们将Karmarkar条件用于内部恒星设置，以便可以获得遵循嵌入I类策略的完整且精确的模型。为此，我们假设各向异性物质的含量以及紧凑型恒星的静态和球对称几何形状。由于Karmarkar嵌入条件产生度量势的关系，因此我们假设度量成分之一的合适形式为，其中和代表常数，是一个自由参数，然后求另一个。我们估算物理参数的值，例如，并利用紧凑型恒星Vela X-1的质量和半径已知值。然后，以图形方式探索所获取模型的有效性，以了解耦合参数的不同值。发现所得到的解决方案在物理上是有趣的并且行为良好。