A Study on the General Relativistic Polytrope of n=5

일반상대론적(一般相對論的) Polytrope(n=5)에 관(關)하여

We have investigated the structure of the general relativistic polytrope(G.R.P.) of n=5. The numerical solutions of the general relativistic Lane-Emden functions ${\upsilon}\;and\;{\theta}$ for the ratio of the central pressure to the central density ${\sigma}=0.1$, 0.3, 0.5 and 0.8333 are plotted graphically. We may summarize the results as follows: 1. As the invariant radius $\bar{\xi}$ increases, the numerical value of the mass parameter ${\upsilon}$ does not approach toward the assymptotic limit, as it does in the classical case $({\upsilon}{\sim}{\sqrt{3}})$, but it increases continuously with progressively smaller rate as compared with the classical case. 2. When $\bar{\xi}$ is less than ${\sim}5.5$, the value of the density function ${\theta}$ drops more rapidly than the classical one, whereas when $\bar{\xi}$ is greater than ${\sim}5.5$, ${\theta}$ becomes greater than the classical value. For the greater values of ${\sigma}$ these phenomena become significant. 3. From the above results it is expected that the equilibrium mass of the G.R.P. of n=5 must be larger than the classical masse $({\sqrt{3}})$ and the mass is more dispersed than the classical configuration (i.e. equilibrium with infinite radius).