Dynamical evolution of self-gravitating models in the Palatini gravity

In this paper, we investigate the evolution of axial and reflection-symmetric fluids using the [Formula: see text] approach in the background of the Palatini [Formula: see text] theory. It is demonstrated that gravitational radiation is not released together with the evolution of the distribution of fluid that adheres to the Tolman criterion for achieving thermal equilibrium. This outcome also conveys the irreversibility connected to gravitational wave emission. Using [Formula: see text] mathematical expression that is obtained from M[Formula: see text]ller–Israel–Stewart (MIS) theory, some thermodynamic features of the problem are discussed. The observational implications are also discussed. It is found that, in addition to being non-dissipative and vorticity-free, the resultant models are also ir-rotational and geodesic, and all of their intricate components disappear.