| 초록 |
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). |
