Collapsing Shear-Free Anisotropic Embedding Star Model in f ( R ) $f(R)$ Gravity

The current paper studied the dynamics of shear-free and spherically symmetric collapsing stars by incorporating the features of anisotropic dissipative fluid in the realm of $f\left(R\right)$ gravity. A complete radiative star model that describes the early static configuration obeying the embedding class 1 approach is generated. To acquittance the exact solutions of the geometric variables, a specific form of pressure anisotropy along with a time-dependent Karmarkar condition is employed, leading to a spacetime solution that seems to be potentially reliable and regular throughout the collapse process. The matching conditions have been thoroughly investigated between the interior geometry and the Vaidya outgoing solution over the junction interface. The physical attributes of our solutions to the Einstein field equations under two viable and cosmologically well-consistent models of $f\left(R\right)$ are manifested. The presented features are in a stable equilibrium state and sustainable to model a dynamic structure of gravitational collapse without forming the black hole.