Some Solutions of Perfect Fluid Static Spherically Symmetric Classes in f(R,T) Theory and Their Related Concircular Vector Fields

In this work we obtained solutions of field equations for perfect fluid spherically symmetric static spacetimes and found their concircular vector fields (CCVFs) in $f(R,T)$ gravity theory. It came out that special classes of these spacetimes possess either $4$-dimensional or $15$-dimensional CCVFs. In [28] the author obtained CCVFs for the same spacetimes in general relativity and it is argued that such spacetimes possess CCVFs of $4-$, $5-$, $6-$ and $15$ dimensions. Our results revealed that the $f(R,T)$ theory restricted the number of CCVFs for the same spacetime. $f(R,T)$ theory allows such spacetimes to admit either the $4$ basic Killing vector fields as CCVFs or compel the spacetime to be conformally flat and admit $15$ CCVFs. We also calculated the energy density, fluid pressure, trace of the energy-momentum tensor $T$, Ricci scalar $R$ and the function $f(R,T)$. It is observed that energy density and fluid pressure of some solutions are related as $p=-\rho$ which means that such particular metrics behave like dark energy models.