标题： 相对论天体物理学中的匹配条件 显示英文标题

标题： Matching conditions in relativistic astrophysics

摘要： 我们提出了一种爱因斯坦-麦克斯韦方程的精确电真空解，其具有无限组多极矩，可用于描述旋转带电质量分布的外部引力场。 我们表明，在缓慢旋转且轻微变形的物体的特殊情况下，外部解可以与属于哈特勒-索恩近似解族的内部解匹配。 为了寻找精确的内部解，我们建议使用曲率本征值的导数来制定一个$C^3-$匹配条件，由此可以推导出可以进行内部和外部时空匹配的最小半径。 我们证明了在具有四极矩的静态质量的特定情况下，$C^3-$匹配的有效性。 相应的内部解是通过数值方法得到的，与外部解的匹配结果给出了质量配置的最小半径。 显示英文摘要

摘要： We present an exact electrovacuum solution of Einstein-Maxwell equations with infinite sets of multipole moments which can be used to describe the exterior gravitational field of a rotating charged mass distribution. We show that in the special case of a slowly rotating and slightly deformed body, the exterior solution can be matched to an interior solution belonging to the Hartle-Thorne family of approximate solutions. To search for exact interior solutions, we propose to use the derivatives of the curvature eigenvalues to formulate a $C^3-$matching condition from which the minimum radius can be derived at which the matching of interior and exterior spacetimes can be carried out. We prove the validity of the $C^3-$matching in the particular case of a static mass with a quadrupole moment. The corresponding interior solution is obtained numerically and the matching with the exterior solution gives as a result the minimum radius of the mass configuration.