- 강용희
- 天文學會誌 = The journal of the Korean Astronomical Society
- 5, n.1
- pp.7-14
- 1972
- 원문 바로보기
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 <TEX>${\upsilon}\;and\;{\theta}$</TEX> for the ratio of the central pressure to the central density <TEX>${\sigma}=0.1$</TEX>, 0.3, 0.5 and 0.8333 are plotted graphically. We may summarize the results as follows: 1. As the invariant radius <TEX>$\bar{\xi}$</TEX> increases, the numerical value of the mass parameter <TEX>${\upsilon}$</TEX> does not approach toward the assymptotic limit, as it does in the classical case <TEX>$({\upsilon}{\sim}{\sqrt{3}})$</TEX>, but it increases continuously with progressively smaller rate as compared with the classical case. 2. When <TEX>$\bar{\xi}$</TEX> is less than <TEX>${\sim}5.5$</TEX>, the value of the density function <TEX>${\theta}$</TEX> drops more rapidly than the classical one, whereas when <TEX>$\bar{\xi}$</TEX> is greater than <TEX>${\sim}5.5$</TEX>, <TEX>${\theta}$</TEX> becomes greater than the classical value. For the greater values of <TEX>${\sigma}$</TEX> 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 <TEX>$({\sqrt{3}})$</TEX> and the mass is more dispersed than the classical configuration (i.e. equilibrium with infinite radius).