标题： 宇宙结构的相对论性维里关系 显示英文标题

标题： Relativistic virial relation for cosmological structures

摘要： 从由分布函数定义的粒子系统的相对论玻尔兹曼方程出发，我们推导了在广义相对论框架下膨胀背景中球对称结构的维里关系。 该维里关系的推广形式随后应用于球对称结构的静态情况，以观察最简单情况下与牛顿关系的差异。 还推导了这种简单情况下的相对论质量-温度关系，该关系可以应用于天体物理学中的致密天体。 我们的普遍维里关系随后应用于膨胀宇宙中结构的非静态情况，在这种情况下出现了一个额外项，通常在存在暗能量的研究中被忽略。 显示英文摘要

摘要： Starting with the relativistic Boltzmann equation for a system of particles defined by a distribution function, we have derived the virial relation for a spherical structure within an expanding background in the context of general relativity. This generalized form of the virial relation is then applied to the static case of a spherically symmetric structure to see the difference in the simplest case to the Newtonian relation. A relativistic Mass-Temperature relation for this simple case is also derived which can be applied to compact objects in astrophysics. Our general virial relation is then applied to the non-static case of a structure within an expanding universe where an extra term, usually missed in studies of structures in the presence of the dark energy, appears.