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The present work is focused on the investigation of the existence of compactstructures describing anisotropic matter distributions within the framework ofmodified gravity theories, specifically f(R,$\mathcal{T}$) gravity theory.Additionally, we have taken f(R,$\mathcal{T}$) as a linear function of theRicci scalar $R$ and the trace of the energy-momentum tensor $\mathcal{T}$ as$f(R,\mathcal{T})$=$R+2\chi\mathcal{T}$,where $\chi$ is a dimensionlesscoupling parameter, and the Lagrangian matter$\mathcal{L}_m=-\frac{1}{3}\left(2p_{t}+p_{r}\right)$, to describe the completeset of field equations for the anisotropic matter distribution. We follow theembedding class one procedure using Eisland condition to obtain a fullspace-time description inside the stellar configuration. Once the space-timegeometry is specified we determine the complete solution of the modifiedEinstein equations by using the MIT bag model equation of state$p_{r}=\frac{1}{3}\left(\rho-4B\right)$ that describes the strange quark matter(SQM) distribution inside the stellar system, where $B$ denotes a bag constant.The physical validity of our anisotropic solution is confirmed by executingseveral physical tests. It is worth mentioning that with the help of theobserved mass values for the various strange star candidates we have predictedthe exact radii by taking different values for $\chi$ and $B$. These predictedradii show monotonic decreasing nature as the parameter $\chi$ is moved from$-0.8$ to $0.8$ progressively. In this case, our anisotropic stellar systembecomes more massive and transforms into more dense compact stars.

Study on anisotropic strange stars in $f(R,T)$ gravity: An embedding approach under simplest linear functional of matter-geometry coupling