Anisotropic fluid spheres in the framework of $f(R,\mathcal{T})$ gravity theory

The main aim of this paper is to obtain analytic relativistic anisotropic spherical solutions in f(R,$\mathcal{T}$) scenario. To do so we use modified Durgapal-Fuloria metric potential and the isotropic condition is imposed in order to obtain the effective anisotropic factor $\tilde{\Delta}$. Besides, a notable and viable election on f(R,$\mathcal{T}$) gravity formulation is taken. Specifically $f(R,\mathcal{T})=R+2\chi\mathcal{T}$, where $R$ is the Ricci scalar, $\mathcal{T}$ the trace of the energy-momentum tensor and $\chi$ a dimensionless parameter. This choice of $f(R,\mathcal{T})$ function modifies the matter sector only, including new ingredients to the physical parameters that characterize the model such as density, radial, and tangential pressure. Moreover, other important quantities are affected such as subliminal speeds of the pressure waves in both radial and transverse direction, observational parameters, for example, the surface redshift which is related with the total mass $M$ and the radius $r_{s}$ of the compact object. Also, a transcendent mechanism like equilibrium through generalized Tolman-Oppenheimer-Volkoff equation and stability of the system are upset. We analyze all the physical and mathematical general requirements of the configuration taking $M=1.04 M_{\odot}$ and varying $\chi$ from $-0.1$ to $0.1$. It is shown by the graphical procedure that $\chi<0$ yields to a more compact object in comparison when $\chi\geq0$ (where $\chi=0.0$ corresponds to general relativity theory) and increases the value of the surface redshift. However, negative values of $\chi$ introduce in the system an attractive anisotropic force (inward) and the configuration is completely unstable (corroborated employing Abreu's criterion). Furthermore, the model in Einstein gravity theory presents cracking while for $\chi>0$ the system is fully stable.