A spherical planetary nebula is described as a geometric model. The nebula itself is considered as a thin-shell, which is visualized as a boundary of two spacetimes. The inner and outer curvature tensors of the thin-shell are found in order to get an expression of the energy-momentum tensor on the thin-shell. The energy density and pressure expressions are derived using the energy-momentum tensor. The time evolution of the radius of the thin-shell is obtained in terms of the energy density. The model is tested by using a simple power function for decreasing energy density and the evolution pattern of the planetary nebula is attained.

中文翻译：

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基于薄壳形式的球形行星状星云演化几何模型

球形行星状星云被描述为几何模型。星云本身被认为是一个薄壳，可视化为两个时空的边界。求薄壳内曲率张量和外曲率张量，以便得到薄壳上的能量-动量张量的表达式。能量密度和压力表达式是使用能量-动量张量导出的。根据能量密度获得薄壳半径的时间演化。通过使用简单的幂函数降低能量密度对该模型进行了测试，得到了行星状星云的演化模式。