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Gravitational collapse of a spherically symmetric homogeneous perfectbarotropic fluid with linear as well as polytropic type Equation of State (EoS)has been investigated in the framework of a linear model of $f(R,T)$ gravity.This modified gravity has the potential to explain the observed cosmicacceleration. The calculations have been done taking the transformed timecoordinate $t \to \sqrt{\frac{\rho_0}{3}} t$, where $\rho_0$ is the initialdensity of the fluid. For linear EoS $p=\omega\rho$, the condition for being atrue singularity, along with sufficient condition for the formation of apparenthorizon covering the singularity has been derived. For a polytrope having theEoS $p=K\rho^{1+\frac{1}{n}}$, the scale factor ($A$) as a function of fluiddensity ($\rho$) has been obtained which is then used to study the dynamics ofthe fluid. Role of the polytropic index ($n$) and the constant ofproportionality ($K$) in the dynamics of the fluid is also studied. A new typeof exotic matter field having varied dependence of scale factor on the density,and having the potential to give rise to bouncing cosmology, provided it is thedominating fluid in the universe, is obtained in this domain and isinvestigated. Energy conditions are discussed.

Dynamics of General Barotropic Stellar Fluid in the Framework of $R+2\alpha T$ Gravity