  In this paper, the quasi static-approximation on the hydrodynamics of compact
objects is proposed in $f(R, T)$ gravity, where $R$ is the scalar curvature and
$T$ is the trace of stress-energy tensor, by exploring the axial and reflection
symmetric space time stuffed with anisotropic and dissipative matter contents.
The set of invariant-velocities is defined to comprehend the concept of quasi
static-approximation. As a consequence, the evolution of compact objects is
shown by analyzing the corresponding modified field, dynamical and scalar
equations in this approximation to evoke all the feasible outcomes.
Furthermore, the significance of kinematical quantities, modified heat-fluxes
and scalar variables are found through the proposed approximation.
