Thermodynamically Consistent Viscous Dissipative Collapse in Rastall Gravity using Causal Transport Equations

A full causal treatment of the dynamics of viscous dissipative gravitational collapse is developed in this study in the framework of Rastall gravity. We extend the Misner-Sharp formalism for gravitational collapse to account for dissipative effects in both the free-streaming and diffusive regimes. The former regime is valid when the characteristic size of the system is much smaller than the typical distance a particle travels before undergoing a collision (its mean free path), and the latter regime is appropriate in optically thick environments where spatial gradients serve as the primary driver of the fluxes. Subsequently, the Israel-Stewart framework couples the dynamical equation to relativistic relaxation equations for the energy flux, viscous shear, and dissipative bulk term, while maintaining the thermodynamic coupling coefficients between viscosity and heat. The obtained results are also contrasted with earlier studies in which those coefficients were omitted and viscous quantities were not described by causal transport equations. Our findings could find applications in specific astrophysical environments and physical conditions.