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

Gravitational collapse of a spherically symmetric homogeneous perfect barotropic 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 cosmic acceleration. The calculations have been done taking the transformed time coordinate $t \to \sqrt{\frac{\rho_0}{3}} t$, where $\rho_0$ is the initial density of the fluid. For linear EoS $p=\omega\rho$, the condition for being a true singularity, along with sufficient condition for the formation of apparent horizon covering the singularity has been derived. For a polytrope having the EoS $p=K\rho^{1+\frac{1}{n}}$, the scale factor ($A$) as a function of fluid density ($\rho$) has been obtained which is then used to study the dynamics of the fluid. Role of the polytropic index ($n$) and the constant of proportionality ($K$) in the dynamics of the fluid is also studied. A new type of 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 the dominating fluid in the universe, is obtained in this domain and is investigated. Energy conditions are discussed.