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We study a specific model of anisotropic strange stars in the modified$f\left(R,\mathcal{T}\right)$-type gravity by deriving solutions to themodified Einstein field equations representing a spherically symmetricanisotropic stellar object. We take a standard assumption that$f(R,\mathcal{T})=R+2\chi\mathcal{T}$, where $R$ is Ricci scalar, $\mathcal{T}$is the trace of the energy-momentum tensor of matter, and $\chi$ is a couplingconstant. To obtain our solution to the modified Einstein equations, wesuccessfully apply the `embedding class 1' techniques. We also consider thecase when the strange quark matter (SQM) distribution is governed by thesimplified MIT bag model equation of state given by$p_r=\frac{1}{3}\left(\rho-4B\right)$, where $B$ is bag constant. We calculatethe radius of the strange star candidates by directly solving the modified TOVequation with the observed values of the mass and some parametric values of $B$and $\chi$. The physical acceptability of our solutions is verified byperforming several physical tests. Interestingly, besides the SQM, another typeof matter distribution originates due to the effect of coupling between thematter and curvature terms in the $f\left(R,\mathcal{T}\right)$ gravity theory.Our study shows that with decreasing the value of $\chi$, the stellar systemsunder investigations become gradually massive and larger in size, turning theminto less dense compact objects. It also reveals that for $\chi<0$ the$f\left(R,\mathcal{T}\right)$ gravity emerges as a suitable theory forexplaining the observed massive stellar objects like massive pulsars,super-Chandrasekhar stars and magnetars, etc., which remain obscure in thestandard framework of General Relativity (GR).

Exploring physical features of anisotropic strange stars beyond standard maximum mass limit in $f\left(R,\mathcal{T}\right)$ gravity