A Study on the General Relativistic Polytrope of n=5

Details A Study on the General Relativistic Polytrope of n=5 A Study on the General Relativistic Polytrope of n=5

Dec 1972

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1972jkas....5....7k&link_type=abstract

Journal of the Korean Astronomical Society, vol. 5, no. 1, p. 7-14

Astronomy and Astrophysics

Astronomy

Scientific paper

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 v 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 xi-bar increases, the numerical value of the mass parameter v does not approach toward the asymptotic limit, as it does in the classical case(v ~ sqrt(3) ), but it increases continuously with progressively smaller rate as compared with the classical case. 2. When xi-bar is less than ~5.5, the value of the density function theta drops more rapidly than the classical one, whereas when xi-bar is greater than ~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 mass(sqrt(3)) and the mass is more dispersed than the classical configuration (i.e. equilibrium with infinite radius).

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