论文标题
在一般相对论中为恒星模型生成函数的线性和riccati方程
Linear and Riccati equations in generating functions for stellar models in general relativity
论文作者
论文摘要
结果表明，对切向压力，各向异性因子和爱因斯坦方程中的径向压力的表达可能是生成恒星模型的函数。当还使用能量密度的表达式时，后者可以结合状态。其他生成的功能基于存在保形运动（尤其是共形平坦度）的条件以及嵌入一级指标的Karmarkar条件。在所有这些情况下，方程是一个公制组件之一的线性一阶微分方程，而另一个方程是另一个方程。后者可以始终转化为二阶均匀线性微分方程。这些结论通过恒星模型的研究中的许多特定例子说明了这些结论。
It is shown that the expressions for the tangential pressure, the anisotropy factor and the radial pressure in the Einstein equations may serve as generating functions for stellar models. The latter can incorporate an equation of state when the expression for the energy density is also used. Other generating functions are based on the condition for the existence of conformal motion (conformal flatness in particular) and the Karmarkar condition for embedding class one metrics. In all these cases the equations are linear first order differential equations for one of the metric components and Riccati equations for the other. The latter may be always transformed into second order homogenous linear differential equations. These conclusions are illustrated by numerous particular examples from the study of stellar models.
