Buchdahl model in f(R, T) gravity: A comparative study with standard Einstein's gravity

This paper is devoted in the study of the hydrostatic equilibrium of stellar structure in the framework of modified $f(R, T)$ gravity theory that allows the non-conservation of energy-momentum, with possible implications for several cosmological and astrophysical issues such as the late-time cosmic acceleration of the universe without appealing to exotic matter fields. For this purpose, we consider the gravitational Lagrangian by taking an arbitrary function of the Ricci scalar and the trace of the stress-energy tensor. We obtain a generic form for the gravitational field equations and derive the field equation for $f(R,T)$ = $R+2 \chi T$. Here we propose a particular metric potential \textit{Buchdahl ansatz} [Phys. Rev. D 116, 1027 (1959)] in principle, of explaining almost all the known analytic solutions to the spherically symmetric, static Einstein equations with a perfect fluid source. For the choice of $f(T)= 2\chi T$ one may observe that the pressure and energy density profiles are markedly different. Important cases, which have been analyzed in detail, are all possible Buchdahl solutions for spherical equilibrium configuration in $f(R, T)$ gravity and compare them with standard gravity theory. We find that Buchdahl's solution in Einstein gravity and $f(R,T)$ gravity behaves in a similar manner but in some situations Einstein gravity displays more pleasing behavior than its $f(R,T)$ counterpart.