标题： 通过嵌入方法在$\mathcal{R}+β\mathcal{R}^{2}$引力中具有物质耦合的各向异性球体 显示英文标题

标题： Anisotropic spheres via embedding approach in $\mathcal{R}+β\mathcal{R}^{2}$ gravity with matter coupling

摘要： 本文的宣言是研究在一种修改的引力理论，即$f(\mathcal{R}, \mathcal{T})$引力背景下，紧致各向异性物质分布，其中$\mathcal{R}$是里奇标量，$\mathcal{T}$是能量-动量张量的迹。 为了达到预期的目标，我们利用了球对称时空，并通过卡马克尔条件采用嵌入类-1解来建模物质分布。 为了计算未确定的约束，考虑了施瓦茨希尔德外部解以及三个不同恒星 LMC X-4、Cen X-3 和 EXO 1785-248 的实验统计数据。 为了评估动力学方程，考虑了一个独特的模型$f(\mathcal{R}, \mathcal{T})=\mathcal{R}+\beta \mathcal{R}^2+\lambda \mathcal{T}$，其中$\beta$和$\lambda$是实常数。 借助修改后的动力学方程，探讨了不同的物理方面。 最后，所有观测中的恒星都是现实的、稳定的，并且没有所有奇点。 显示英文摘要

摘要： The manifesto of the current article is to investigate the compact anisotropic matter profiles in the context of one of the modified gravitational theories, known as $f(\mathcal{R}, \mathcal{T})$ gravity, where $\mathcal{R}$ is a Ricci Scalar and $\mathcal{T}$ is the trace of the energy-momentum tensor. To achieve the desired goal, we capitalized on the spherical symmetric space-time and utilized the embedding class-1 solution via Karmarkar's condition in modeling the matter profiles. To calculate the unidentified constraints, Schwarzschild exterior solution along with experimental statistics of three different stars LMC X-4, Cen X-3, and EXO 1785-248 are taken under consideration. For the evaluation of the dynamical equations, a unique model $f(\mathcal{R}, \mathcal{T})=\mathcal{R}+\beta \mathcal{R}^2+\lambda \mathcal{T}$ has been considered, with $\beta$ and $\lambda$ being the real constants. Different physical aspects have been exploited with the help of modified dynamical equations. Conclusively, all the stars under observations are realistic, stable, and are free from all singularities.