标题： 对符合平直度的辐射星体的李对称性 显示英文标题

标题： Lie symmetries for a conformally flat radiating star

摘要： 我们考虑一个在共形平坦时空中的相对论性辐射球状星体。 特别是我们研究星体边界处径向压强与热通量之间的连接条件，这是一个非线性偏微分方程。 识别出使该方程保持不变的李对称生成元，并生成一个最优系统。 最优系统中的每个元素用于将偏微分方程约化为常微分方程，并进一步进行分析。 我们识别出边界条件的新类别精确解。 有两类解是有趣的。 第一类解依赖于一个自相似变量。 第二类解在时空变量中是可分离的。 显示英文摘要

摘要： We consider a relativistic radiating spherical star in conformally flat spacetimes. In particular we study the junction condition relating the radial pressure to the heat flux at the boundary of the star which is a nonlinear partial differential equation. The Lie symmetry generators that leave the equation invariant are identified and we generate an optimal system. Each element of the optimal system is used to reduce the partial differential equation to an ordinary differential equation which is further analysed. We identify new categories of exact solutions to the boundary conditions. Two classes of solutions are of interest. The first class depends on a self similar variable. The second class is separable in the spacetime variables.