In this paper, we have employed the time-dependent Karmarkar condition to the shear-free nonstatic radiative model undergoing dissipative gravitational collapse (GC) with anisotropic radial heat flux distribution in the metric [Formula: see text] formalism. We have obtained the final solutions of the [Formula: see text] field equations under the consideration of three viable models [Formula: see text], [Formula: see text] and [Formula: see text]-[Formula: see text], which are physically realistic at both the early and late-time cosmological epochs. In this relevance, the Karmarkar condition together with boundary condition presents a complete radiating star model which are experienced by the initial static configuration. The matching conditions have been derived between the exterior Vaidya metric and interior line-element across the boundary three surface which permits to study the physical credibility of our radiating star model. Afterwards, we have comprehensively discussed the physical significance of the matter variables and causal thermodynamical profile by graphical representation for our radiating star object. Moreover, we have also studied that the GC proceeds without the appearance of the horizon, i.e. the model is free of horizon.

中文翻译：

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在 f(R) 重力下通过 Karmarkar 条件的无剪切辐射坍塌模型

在本文中，我们将时间相关的 Karmarkar 条件应用于经历耗散引力坍缩 (GC) 的无剪切非静态辐射模型，该模型在度量 [公式：见文本] 形式中具有各向异性径向热通量分布。我们在考虑三种可行模型[公式：见文]、[公式：见文]和[公式：见文]-[公式：见文]的情况下，得到了[公式：见文]场方程的最终解，这在早期和晚期宇宙学时代都是物理现实的。在此相关性中，Karmarkar 条件与边界条件一起呈现了一个完整的辐射星模型，该模型由初始静态配置所经历。外部 Vaidya 度量和跨边界三表面的内部线元之间的匹配条件已经得出，这允许研究我们的辐射星模型的物理可信度。之后，我们通过图形表示我们的辐射星体，全面讨论了物质变量和因果热力学剖面的物理意义。此外，我们还研究了GC在没有地平线出现的情况下进行，即模型没有地平线。