Evolution of non-static fluid for irreversible gravitational radiation in Palatini F(R) gravity

In this manuscript, we focus on a comprehensive investigation of non-static axially symmetric fluid distributions in the background of Palatini F(R) gravity. To do so, a general framework is established to examine the irreversible nature of gravitational radiation. To begin with, modified Einstein field equations (EFE), kinematical variables, and transport equations are derived using connection symbols which help understand the thermodynamic characteristics of considered compact systems. Afterwards, we analyze the Tolman criteria for the thermodynamic equilibrium of a non-static axially symmetric fluid distribution and deduce that non-static fluids do not arise from the emission of gravitational radiation in Palatini F(R) gravitational theory. This result highlights that irreversibility is linked to gravitational wave emission and supports Bondi's conjecture. Subsequently, we explore the notable results that arise from this hypothesis in the Palatini F(R) formalism.