Expansion free spherical anisotropic solutions

Abstract

We investigate the behavior of expansion free collapsing fluids, as studied by L. Herrera, A. Di Prisco and J. Ospino [Symmetry 15 (2023) 754], in the framework of [Formula: see text] gravity, which represents a modification of Einstein’s general relativity by establishing a function of the Ricci scalar [Formula: see text] in the gravitational action. We explore dynamical equations from Bianchi identities that demonstrate the motion and evolution of physical systems under the influence of gravitational fields. We match the inner and outer geometries of spacetime on the hypersurface to develop junction conditions by using the Misner–Sharp formalism. This allows us to identify the connection between mass functions for the inner and outer space as well as the relationship for heat flux [Formula: see text] and radial pressure [Formula: see text]. We also investigate analytical solutions of dissipative fluid distribution that fulfill the vanishing expansion condition together with the vanishing complexity factor constraint. For this, we introduce new constraints that permit the integration of the complex system in [Formula: see text] gravity. Next, we extract a set of differential equations that explain the dynamical structure of the dissipative spheres both in geodesic and non-geodesic fluids. Furthermore, we explore the physical characteristics of the obtained solutions, such as heat flux, energy density, shear stress, fluid’s temperature along with tangential and radial pressure, to assess their viability in describing real astrophysical systems.