The Exact Solutions of Distribution of the Density of Material in A Relativistic Polytrope with A Compact Core

On the basis of the paper(4),in this paper,we have re-discussed in detail the distribution of the density of material in a relativistic polytrope with a compact core.We solved the Euler equation and got some exact analytical solutions. Our results show that the distribution of the density of material in a relativistic polytrope with a compact core is inversely proportional to the cube of radius r (that is,n(r)∝r^-3)and it is different from the isothermal gas sphere(n∝r^-2). Thus, using observation one can distinguish between an isothermal gas. sphere (n∝r^-2)and a relativistic polytrope with a compact core.