标题： 星系的相对论模型 显示英文标题

标题： Relativistic Models of Galaxies

摘要： 采用圆柱坐标下同向度量的一种特殊形式，构建了可以被解释为广义相对论版本的一些在牛顿引力中用于建模星系三维物质分布的熟知的势密度对。 计算了前两个宫本-长井势以及由佐藤提出的特定势的能量-动量张量分量。 这三个势产生的物质分布满足所有拉力均为压力，并且在自由参数的某些范围内满足所有能量条件。 计算了其中一个势的少数非平面测地线轨道，并与牛顿情况进行了比较。 此外，旋转也被纳入模型，并通过使用同向坐标下的克尔度量近似形式，以一阶修正计算了源旋转对旋转曲线的影响。 显示英文摘要

摘要： A special form of the isotropic metric in cylindrical coordinates is used to construct what may be interpreted as the General Relativistic versions of some wellknown potential-density pairs used in Newtonian gravity to model three-dimensional distributions of matter in galaxies. The components of the energy-momentum tensor are calculated for the first two Miyamoto-Nagai potentials and a particular potential due to Satoh. The three potentials yield distributions of matter in which all tensions are pressures and all energy conditions are satisfied for certain ranges of the free parameters. A few non-planar geodesic orbits are computed for one of the potentials and compared with the Newtonian case. Rotation is also incorporated to the models and the effects of the source rotation on the rotation profile are calculated as first order corrections by using an approximate form of the Kerr metric in isotropic coordinates.