The objective of this paper is to investigate the validity conditions for the generalized second law of thermodynamics, and the universal relations for multi-horizon dynamical spacetime. It is found that there are three horizons of McVittie universe termed as event horizon, cosmological apparent horizon, and virtual horizon. The mass-dependent and mass-independent area product relations are formulated in terms of areas of the dynamical event horizon, cosmological horizon and virtual horizon. It is noted that whereas the area sum relation is mass independent, the area product relation is explicitly mass dependent. Moreover, we have also analyzed and listed explicit mass-independent and mass-dependent relations.

中文翻译：

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广义第二定律与宇宙黑洞的普遍关系

本文的目的是研究热力学广义第二定律的有效性条件，以及多水平动力学时空的普遍关系。发现麦克维迪宇宙存在三个视野，分别称为事件视野，宇宙学表观视野和虚拟视野。根据动力学事件视界，宇宙学视界和虚拟视界的区域来表述质量相关和质量独立的区域积关系。注意，尽管面积和关系与质量无关，但面积乘积关系却明显与质量有关。此外，我们还分析并列出了明确的质量独立和质量依赖关系。