标题： 由李对称性生成的测地线模型 显示英文标题

标题： Geodesic models generated by Lie symmetries

摘要： 我们研究剪切和膨胀的球对称辐射星体边界处压力与热通量之间的连接条件，当流体粒子沿测地线运动时。 保持连接条件不变的李对称生成元被确定，并生成了最优系统。 我们使用最优系统的每个元素将偏微分方程转化为常微分方程。 发现了在李点无限小对称作用下具有群不变性的新精确解。 我们得到了行波解和自相似解等解族。 引力势以初等函数形式给出，所有情况下线元都可以显式给出。 我们证明弗里德曼尘埃模型作为特殊情况被恢复，并且可以将我们的结果与早期的研究联系起来。 显示英文摘要

摘要： We study the junction condition relating the pressure to the heat flux at the boundary of a shearing and expanding spherically symmetric radiating star when the fluid particles are travelling in geodesic motion. The Lie symmetry generators that leave the junction condition invariant are identified and the optimal system is generated. We use each element of the optimal system to transform the partial differential equation to an ordinary differential equation. New exact solutions, which are group invariant under the action of Lie point infinitesimal symmetries, are found. We obtain families of traveling wave solutions and self-similar solutions, amongst others. The gravitational potentials are given in terms of elementary functions, and the line elements can be given explicitly in all cases. We show that the Friedmann dust model is regained as a special case, and we can connect our results to earlier investigations.