Our study illuminates the effects of gravitational collapse by considering heat flux anisotropic matter sources within the framework of the $f\left(R\right)$ theory of gravity. We assume the non-static spherically symmetric configuration to narrate the nature of the interior spacetime and match it with the Vaidya exterior geometry. Further, we employ the well-known Karmarkar condition, as it reduces the solution-generating method of field equations to a single metric potential. To ensure the viability of our collapsing system, a comprehensive graphical analysis is presented in the context of the Logarithmic-corrected $R^2$ gravity model. Our investigation argues that there are no traces of trapped surfaces in the collapsing procedure. Thus, naked singularity and black hole are not the final fate of the gravitational collapse.

我们的研究通过在框架内考虑热通量各向异性物质源来阐明引力坍缩的影响。 $F\left(\mathrm{电阻}\right)$引力理论。我们假设非静态球对称配置来叙述内部时空的性质并将其与 Vaidya 外部几何形状相匹配。此外，我们采用了著名的 Karmarkar 条件，因为它将场方程的解生成方法简化为单个度量势。为了确保我们的折叠系统的可行性，在对数校正的上下文中提供了全面的图形分析${\mathrm{电阻}}^2$重力模型。我们的调查认为，在坍塌过程中没有被困表面的痕迹。因此，裸奇点和黑洞并不是引力坍缩的最终命运。