This paper is devoted to develop compact stellar configuration and to evaluate exact interior solutions in the background of $f(T,\mathcal{T})$ gravity, where $T$ be the torsion scalar and $\mathcal{T}$ be the trace of energy momentum tensor. We develop a new set up for embedding class I model under well-known Karmarkar condition for LMC X-4 and Vela X-1 compact stars using specific linear function $f(T,\mathcal{T})=\alpha T\left(r\right)+\beta \mathcal{T}\left(r\right)+\Phi$, where $\alpha ,\beta$ are any arbitrary constants and $\Phi$ be the cosmological constant. Considering static spherically symmetric space–time with perfect fluid distribution, we construct the background field equations, which describe the interior of a fluid sphere. To examine the physical viability of the obtained solutions, we have discussed all the relevant physical quantities (density, pressure, equation of state parameter, square speed of sound and equilibrium condition) analytically and graphically. It is observed that our calculated interior solutions for compact stars showed consistency with all necessary and sufficient physical conditions and hence are physically acceptable and interesting.

本文致力于开发紧凑的恒星配置，并在背景下评估确切的内部解决方案。 $F（Ť，\mathcal{Ť}）$ 重力在哪里 $Ť$ 是扭转标量， $\mathcal{Ť}$是能量动量张量的踪迹。我们为LMC X-4和Vela X-1紧凑型恒星使用特定的线性函数开发了一种在已知的Karmarkar条件下嵌入I类模型的新设置$F（Ť，\mathcal{Ť}）=\alpha Ť（\mathrm{[R}）+\beta \mathcal{Ť}（\mathrm{[R}）+\Phi$，在哪里 $\alpha ，\beta$ 是任意常数，并且 $\Phi$是宇宙常数。考虑具有完美流体分布的静态球对称时空，我们构建了描述流体球内部的背景场方程。为了检查所获得解决方案的物理可行性，我们通过分析和图形方式讨论了所有相关物理量（密度，压力，状态参数方程，平方声速和平衡条件）。可以观察到，我们为紧凑型恒星计算的内部解决方案在所有必要和充分的物理条件下均显示出一致性，因此在物理上是可接受的且令人感兴趣。