Exploring Dissipative Gravitational Collapse of Viscous Fluids in Extended Non-minimally Coupled Gravity

We study the gravitational collapse and dynamical instability of a viscous dissipative fluid via the Israel-Stewart formalism in [Formula: see text] gravity, where [Formula: see text], [Formula: see text] and [Formula: see text] are the Ricci scalar, matter Lagrangian, and trace of the energy-momentum tensor, respectively. Originally formulated for perfect fluids, the classic Misner-Sharp formalism for gravitational collapse in spherically symmetric models is now extended to incorporate specific viscous dissipative effects like shear viscosity. Dissipative fluxes are handled using two complementary regimes: the streaming-out approximation (system scale much smaller than the mean free path) and the diffusion approximation (optically thick media, where gradients drive the fluxes). Having derived the dynamical equations, we compare our results with those of the earlier studies that omitted the factors mentioned above and did not account for dissipative flow parameters. Our findings may prove applicable under specific physical conditions encountered in astrophysical contexts.