Dynamical behavior of the Tolman metrics in f(R,T) gravity

Abstract

We analyze the behavior of well-known stellar models within the context of $f(R,T)$ modified theory of gravity, in which the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$ and the trace of the energy-momentum tensor $T$, namely $f(R,T)=R+2\ensuremath{\chi}T$ for some constant $\ensuremath{\chi}$. The equation of pressure isotropy in this theory is identical to that of the standard Einstein theory therefore all known metric potentials solving Einstein's equations are valid here. However, the pressure and energy density profiles are markedly different due to the presence of the term $2\ensuremath{\chi}T$. The exact solutions to the corresponding static spherically symmetric field equations with a perfect fluid source are the well known Tolman solutions [Phys. Rev. 55, 364 (1939)] in general relativity. To support the theoretical results, graphical representation are employed to investigate the physical viability of compact stars. Specifically we study the density and pressure profiles, the sound speed behavior as well as the energy conditions and mass behavior where appropriate. It is found that in some cases the $f(R,T)$ model displays more pleasing behavior than its Einstein counterpart while in other cases the behavior is similar. In no case does the $2\ensuremath{\chi}T$ addition negatively impact the model's behavior.