The Vaidya metric is important in describing the exterior spacetime of a radiating star and for describing astrophysical processes. In this paper we study embedding properties of the generalized Vaidya metric. We had obtained embedding conditions, for embedding into 5-dimensional Euclidean space, by two different methods and solved them in general. As a result we found the form of the mass function which generates a subclass of the generalized Vaidya metric. Our result is purely geometrical and may be applied to any theory of gravity. When we apply Einstein’s equations we find that the embedding generates an equation of state relating the null string density to the null string pressure. The energy conditions lead to particular metrics including the anti/de Sitter spacetimes.

中文翻译：

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嵌入Vaidya几何

Vaidya度量对于描述辐射恒星的外部时空以及描述天体物理过程非常重要。在本文中，我们研究了广义Vaidya度量的嵌入特性。我们已经通过两种不同的方法获得了嵌入到5维欧几里德空间中的嵌入条件，并对其进行了总体求解。结果，我们发现了质量函数的形式，该函数生成了广义Vaidya度量的子类。我们的结果纯粹是几何的，可以应用于任何重力理论。当我们应用爱因斯坦方程时，我们发现该嵌入生成了一个状态方程，将空弦密度与空弦压力相关联。能量条件导致特定的度量标准，包括反Sitter时空。