Non-Singular gravitational collapse in generalized Rastall theory

In the present work we study the process of gravitational collapse of a homogeneous dust in the framework of generalized Rastall gravity. In this theory, the Rastall coupling parameter is a variable and since this parameter represents the measure of mutual interaction between matter and geometry it is expected that such an interaction affects the collapse dynamics and its end product. Motivated by this idea, we search for non-singular solutions for the interior spacetime of the collapsing dust fluid. We observe that this scenario is feasible for a suitable choice of the functionality of the coupling parameter such that the singularity present in homogeneous dust collapse is replaced by a non-singular bounce where the energy density and spacetime curvature are finite. We also observe that such a variable coupling affects the dynamics of apparent horizon so that, in comparison to the singular case where the apparent horizon covers the spacetime singularity, the apparent horizon can be delayed or failed to form providing thus the possibility of detecting the bouncing object by external observers.