论文标题
牛顿后球面对称积聚
Post-Newtonian Spherically Symmetrical Accretion
论文作者
论文摘要
The objetive of this work is to investigate the influence of the corrections to the spherical symmetrical accretion of an infinity gas cloud characterized by a polytropic equation into a massive object due to the post-Newtonian approximation.The post-Newtonian corrections to the critical values of the flow velocity, sound velocity and radial distance are obtained from the system of hydrodynamics equations in spherical coordinates.牛顿后近似值积聚的临界点与牛顿理论中的跨性别点不符。获得马赫数的方程是作为无量纲径向坐标的函数获得的。据认为，声速度的比率远远超出了巨大的身体和光速为$ a_ \ in_ \ infty/c = 10^{ - 2} $。对溶液的分析导致了以下结果：牛顿和牛顿后积聚的马赫数实际上具有相同的临界径向距离径向距离的值；通过降低径向距离，牛顿积聚的马赫数大于牛顿后积聚的距离。马赫数通过降低特定热量的比率增加。当比率$ a_ \ indy/c \ ll10^{ - 2} $时，牛顿和牛顿后马赫数之间的差异是无关紧要的。对于径向距离的最低值，校正术语在牛顿后伯努利方程中的效果更具感知性，而$ a_ \ infty/c> 10^{ - 2} $的解决方案不会导致关键点的连续流入和流速。将解决方案与从相对论的伯努利方程进行的解决方案的比较表明，马赫数与前者的径向距离的依赖性大于牛顿后距离。
The objetive of this work is to investigate the influence of the corrections to the spherical symmetrical accretion of an infinity gas cloud characterized by a polytropic equation into a massive object due to the post-Newtonian approximation.The post-Newtonian corrections to the critical values of the flow velocity, sound velocity and radial distance are obtained from the system of hydrodynamics equations in spherical coordinates. The critical point in the post-Newtonian approximation accretion does not correspond to the transonic point like in Newtonian theory. An equation for the Mach number was obtained as a function of a dimensionless radial coordinate. It was considered that the ratio of the sound velocity far the massive body and the speed of light was of order $a_\infty/c=10^{-2}$. The analysis of the solution led to following results: the Mach number for the Newtonian and post-Newtonian accretion have practically the same values for radial distances of order of the critical radial distance; by decreasing the radial distance the Mach number for the Newtonian accretion is bigger than the one for the post-Newtonian accretion; the Mach number increases by decreasing the ratio of the specific heats; the difference between the Newtonian and post-Newtonian Mach numbers when the ratio $a_\infty/c\ll10^{-2}$ is insignificant. The effect of the correction terms in post-Newtonian Bernoulli equation is more perceptive for the lowest values of the radial distance, and the solutions for $a_\infty/c>10^{-2}$ does not lead to a continuous inflow and outflow velocity at the critical point. A comparison of the solutions with those that follow from a relativistic Bernoulli equation shows that the dependence of the Mach number with the radial distance of the former is bigger than the post-Newtonian ones.
